Soc 722

Spring 2025

Stephen Vaisey

Introduction

Objective

This is the first in a two-course sequence designed to help you become competent quantitative researchers in sociology.

This includes learning proper decision making, explanation, computation, visualization, and interpretation.

Schedule

We will normally meet Tuesdays. Please note that we will be meeting on the following Thursdays (not Tuesdays) because of my travel schedule:

  • today
  • January 30
  • February 6
  • February 13
  • March 20

Final exam

The exam will be remote on April 30 from 9am-12pm.

Syllabus

The syllabus is here. Please be sure to read it.

Packages needed

You will need the following packages to run everything in this course.

Questions?

Data and Variables

Data structure

country continent year lifeExp pop gdpPercap
Afghanistan Asia 1952 28.801 8425333 779.4453
Afghanistan Asia 1957 30.332 9240934 820.8530
Afghanistan Asia 1962 31.997 10267083 853.1007
Afghanistan Asia 1967 34.020 11537966 836.1971
Afghanistan Asia 1972 36.088 13079460 739.9811
Afghanistan Asia 1977 38.438 14880372 786.1134
Afghanistan Asia 1982 39.854 12881816 978.0114
Afghanistan Asia 1987 40.822 13867957 852.3959
Afghanistan Asia 1992 41.674 16317921 649.3414
Afghanistan Asia 1997 41.763 22227415 635.3414

Tidy format: columns contain variables, each row is an observation.

Untidy data

country continent lifeExp_1952 lifeExp_1957 lifeExp_1962 lifeExp_1967 lifeExp_1972 lifeExp_1977 lifeExp_1982 lifeExp_1987 lifeExp_1992 lifeExp_1997 lifeExp_2002 lifeExp_2007 pop_1952 pop_1957 pop_1962 pop_1967 pop_1972 pop_1977 pop_1982 pop_1987 pop_1992 pop_1997 pop_2002 pop_2007 gdpPercap_1952 gdpPercap_1957 gdpPercap_1962 gdpPercap_1967 gdpPercap_1972 gdpPercap_1977 gdpPercap_1982 gdpPercap_1987 gdpPercap_1992 gdpPercap_1997 gdpPercap_2002 gdpPercap_2007
Afghanistan Asia 28.801 30.332 31.997 34.020 36.088 38.438 39.854 40.822 41.674 41.763 42.129 43.828 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 25268405 31889923 779.4453 820.8530 853.1007 836.1971 739.9811 786.1134 978.0114 852.3959 649.3414 635.3414 726.7341 974.5803
Albania Europe 55.230 59.280 64.820 66.220 67.690 68.930 70.420 72.000 71.581 72.950 75.651 76.423 1282697 1476505 1728137 1984060 2263554 2509048 2780097 3075321 3326498 3428038 3508512 3600523 1601.0561 1942.2842 2312.8890 2760.1969 3313.4222 3533.0039 3630.8807 3738.9327 2497.4379 3193.0546 4604.2117 5937.0295
Algeria Africa 43.077 45.685 48.303 51.407 54.518 58.014 61.368 65.799 67.744 69.152 70.994 72.301 9279525 10270856 11000948 12760499 14760787 17152804 20033753 23254956 26298373 29072015 31287142 33333216 2449.0082 3013.9760 2550.8169 3246.9918 4182.6638 4910.4168 5745.1602 5681.3585 5023.2166 4797.2951 5288.0404 6223.3675
Angola Africa 30.015 31.999 34.000 35.985 37.928 39.483 39.942 39.906 40.647 40.963 41.003 42.731 4232095 4561361 4826015 5247469 5894858 6162675 7016384 7874230 8735988 9875024 10866106 12420476 3520.6103 3827.9405 4269.2767 5522.7764 5473.2880 3008.6474 2756.9537 2430.2083 2627.8457 2277.1409 2773.2873 4797.2313
Argentina Americas 62.485 64.399 65.142 65.634 67.065 68.481 69.942 70.774 71.868 73.275 74.340 75.320 17876956 19610538 21283783 22934225 24779799 26983828 29341374 31620918 33958947 36203463 38331121 40301927 5911.3151 6856.8562 7133.1660 8052.9530 9443.0385 10079.0267 8997.8974 9139.6714 9308.4187 10967.2820 8797.6407 12779.3796
Australia Oceania 69.120 70.330 70.930 71.100 71.930 73.490 74.740 76.320 77.560 78.830 80.370 81.235 8691212 9712569 10794968 11872264 13177000 14074100 15184200 16257249 17481977 18565243 19546792 20434176 10039.5956 10949.6496 12217.2269 14526.1246 16788.6295 18334.1975 19477.0093 21888.8890 23424.7668 26997.9366 30687.7547 34435.3674
Austria Europe 66.800 67.480 69.540 70.140 70.630 72.170 73.180 74.940 76.040 77.510 78.980 79.829 6927772 6965860 7129864 7376998 7544201 7568430 7574613 7578903 7914969 8069876 8148312 8199783 6137.0765 8842.5980 10750.7211 12834.6024 16661.6256 19749.4223 21597.0836 23687.8261 27042.0187 29095.9207 32417.6077 36126.4927
Bahrain Asia 50.939 53.832 56.923 59.923 63.300 65.593 69.052 70.750 72.601 73.925 74.795 75.635 120447 138655 171863 202182 230800 297410 377967 454612 529491 598561 656397 708573 9867.0848 11635.7995 12753.2751 14804.6727 18268.6584 19340.1020 19211.1473 18524.0241 19035.5792 20292.0168 23403.5593 29796.0483
Bangladesh Asia 37.484 39.348 41.216 43.453 45.252 46.923 50.009 52.819 56.018 59.412 62.013 64.062 46886859 51365468 56839289 62821884 70759295 80428306 93074406 103764241 113704579 123315288 135656790 150448339 684.2442 661.6375 686.3416 721.1861 630.2336 659.8772 676.9819 751.9794 837.8102 972.7700 1136.3904 1391.2538
Belgium Europe 68.000 69.240 70.250 70.940 71.440 72.800 73.930 75.350 76.460 77.530 78.320 79.441 8730405 8989111 9218400 9556500 9709100 9821800 9856303 9870200 10045622 10199787 10311970 10392226 8343.1051 9714.9606 10991.2068 13149.0412 16672.1436 19117.9745 20979.8459 22525.5631 25575.5707 27561.1966 30485.8838 33692.6051
Benin Africa 38.223 40.358 42.618 44.885 47.014 49.190 50.904 52.337 53.919 54.777 54.406 56.728 1738315 1925173 2151895 2427334 2761407 3168267 3641603 4243788 4981671 6066080 7026113 8078314 1062.7522 959.6011 949.4991 1035.8314 1085.7969 1029.1613 1277.8976 1225.8560 1191.2077 1232.9753 1372.8779 1441.2849
Bolivia Americas 40.414 41.890 43.428 45.032 46.714 50.023 53.859 57.251 59.957 62.050 63.883 65.554 2883315 3211738 3593918 4040665 4565872 5079716 5642224 6156369 6893451 7693188 8445134 9119152 2677.3263 2127.6863 2180.9725 2586.8861 2980.3313 3548.0978 3156.5105 2753.6915 2961.6997 3326.1432 3413.2627 3822.1371

Types of variables

Ratio dollars; points (e.g., basketball)
Interval degrees Celsius
Ordinal clothing sizes; Likert scales
Nominal race; sex; country

The first two types are continuous or numeric. The second two types are categorical. Ordinal variables are often treated as numeric and this is usually fine.

Let’s investigate this using the gapminder data. First of all, we’ll keep only the most recent (2007) data.

d <- gapminder |>               
  filter(year == max(year)) |> # keep 2007
  select(-year)                # don't need column

country continent lifeExp pop gdpPercap
Afghanistan Asia 43.828 31889923 974.5803
Albania Europe 76.423 3600523 5937.0295
Algeria Africa 72.301 33333216 6223.3675
Angola Africa 42.731 12420476 4797.2313
Argentina Americas 75.320 40301927 12779.3796
Australia Oceania 81.235 20434176 34435.3674
Austria Europe 79.829 8199783 36126.4927
Bahrain Asia 75.635 708573 29796.0483
Bangladesh Asia 64.062 150448339 1391.2538
Belgium Europe 79.441 10392226 33692.6051

What kinds of variables are these?

The origins of “statistics”

The word statistics comes from the fact that it was information about the state. We’ll focus on information like this for now rather than thinking about samples of individuals.

Visualization basics

Consider two types of plots

  • univariate plots

  • bivariate plots

These are also types of distributions.

Univariate plots

Density plot

ggplot(d,
       aes(x = gdpPercap)) +
  geom_density()

Density plot

Histogram (1)

ggplot(d,
       aes(x = gdpPercap)) +
  geom_histogram(binwidth = 5000,
                 boundary = 0,
                 color = "white")

Histogram (1)

Histogram (2)

ggplot(d,
       aes(x = lifeExp)) +
  geom_histogram(binwidth = 5,
                 boundary = 0,
                 color = "white")

Histogram (2)

Bar graph (univariate)

ggplot(d,
       aes(x = continent)) +
  geom_bar()

Bar graph (univariate)

Bivariate plots

Scatter plot

ggplot(d,
       aes(x = gdpPercap,
           y = lifeExp)) +
         geom_point()

Scatter plot

Bar graph (bivariate)

d |> 
  group_by(continent) |> 
  summarize(GDP = mean(gdpPercap)) |>
  ggplot(aes(x = continent,
             y = GDP)) +
  geom_bar(stat = "identity")

Bar graph (bivariate)

Strip plot

ggplot(d,
       aes(x = gdpPercap,
           y = continent)) +
  geom_point(alpha = .3)

Strip plot

Jittered strip plot

ggplot(d,
       aes(x = gdpPercap,
           y = continent)) +
  geom_jitter(height = .1,
              width = .1,
              alpha = .2)

Jittered strip plot

Time plots (bivariate)

Let’s go back to the full data and look at trends in Oceania.

gapminder |> 
  filter(continent == "Oceania") |> 
  ggplot(aes(x = year,
             y = lifeExp,
             group = country,
             color = country)) +
  geom_line()

Time plots (bivariate)

Your turn!

Homework

  1. Set up a public GitHub repository for this class
  2. Share it with the class on Slack
  3. Create a Quarto document (HW1.qmd) making several visualizations using data of your choice
  4. Render it to html (HW1.html)
  5. Push it to your repository by midnight before the next meeting

Surveys, samples, and probability

Populations and samples

Studying populations is nice:

  • all countries in the world
  • all states in the US
  • all cities in a state

However, we cannot study (say) all adults in a country. So we usually work with samples. This raises the issue of using samples to make inferences about populations.

Simple random sampling

Sampling where every eligible case has an equal probability of selection.

Note

In real-life surveys, simple random sampling is pretty uncommon. But it’s important as a baseline!

Simulations

We can use simulations to build intuition about sampling.

A simulation is when we make up “true data”, hide it from ourselves, and see how well we can figure out the the truth using some procedure.

Simple survey

Imagine a city of 100,000 adults. Of these, 70,000 (i.e., 70%) have at least one child.

How close could we get to this number by drawing different random samples?

A first simulation

Let’s set up the “true” population:

population <- tibble(id = 1:1e5) |> # initialize with 100K rows
  mutate(parent = if_else(id <= 70000, "Yes", "No"))  # first 70K "yes"

This simple code makes the first 70,000 rows “yes” and the next 30,000 “no.” We now know the “truth”, which we can use for comparison.

Visualizing the population

Data types

Because of the way we created it, parent will be a character <chr> variable. We often use 1 to mean “yes” and 0 to mean “no” in statistics. We could add a numeric version of parent as follows.

population <- population |> 
  mutate(parent_num = if_else(parent == "Yes", 1L, 0L))

Tip

Assigning an object to its “old” name allows you to add things to the original object. In this case, we are adding a new column, parent_num.

Checking data type

We can use glimpse() to easily see what type of variable things are.

glimpse(population)
Rows: 100,000
Columns: 3
$ id         <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15…
$ parent     <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", …
$ parent_num <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…

Tip

glimpse() is very useful. It shows you your data “sideways” so you can see information about all the columns (which are shown as rows).

Implications of data type

Data type affects what we can do to a variable (or column). For example, we can take the mean (average) of a set of numbers but we can’t take the mean of a set of characters.

population |>
  summarize(mean1 = mean(parent),
            mean2 = mean(parent_num))
# A tibble: 1 × 2
  mean1 mean2
  <dbl> <dbl>
1    NA   0.7

Note

In R, NA stands for “not available” and means that the data are missing. This cell is missing because what we asked for couldn’t be calculated.

Aside: doing stuff to a variable

We can pick out a column to operate on in two ways:

tidyverse

population |> 
  pull(parent_num) |> 
  mean()
[1] 0.7

base R

mean(population$parent_num)
[1] 0.7

Now back to our story…

Parameters and statistics

In our city, 70% is the population parameter because exactly 70,000 out of 100,000 people actually have at least one child.

We can’t afford to ask everyone, though. So what if we asked, say, 1000 randomly selected adults. Then we could compute the proportion of the sample that has a child. This would be a sample statistic. We use sample statistics to make inferences about population parameters.

Drawing a sample

set.seed(722)
my_sample <- population |> 
  slice_sample(n = 1000,
               replace = FALSE)

Sampling is a random process. We will get a different result every time. By using set.seed(), we ensure we get the same “random” result every time the code is run.

Note

Sampling theory is based on sampling with replacement. However, to make it more straightforward, we will use sampling without replacement here.

The sample statistic

To estimate the population proportion, we will use the sample proportion.

my_sample |> 
  group_by(parent) |> 
  summarize(n = n())
# A tibble: 2 × 2
  parent     n
  <chr>  <int>
1 No       318
2 Yes      682

In our sample, 682 people are parents. This is 68.2%, which isn’t exactly the 70% in the population. This is because we randomly sampled from our population. It could be higher or lower.

Repeating the experiment

In real life, we only get to sample once. Sampling is expensive! But since this is just a simulation, we can ask what would happen if we sampled 1000 people many, many times.

A custom function

We can first make a function that does what we want once. This is hard at first but usually pays off.

get_count <- function(n = 1000) {       # default n = 1000
  slice_sample(population, n = n) |>    # take a sample
    summarize(sum = sum(parent_num)) |> # count the parents
    as.integer()                        # save the number
}

Tip

If you run all the code up to here, you can call get_count() interactively in the console many times to get a feel for it.

Iterating

This would seem to make sense, but it doesn’t work.

set.seed(722)
my_bad_samples <- tibble(
  sample_id = 1:100,
  samp_count = get_count(n = 1000))
head(my_bad_samples)
# A tibble: 6 × 2
  sample_id samp_count
      <int>      <int>
1         1        682
2         2        682
3         3        682
4         4        682
5         5        682
6         6        682

Iterating with rowwise()

set.seed(722)
my_samples <- tibble(
  sample_id = 1:100) |> 
  rowwise() |> 
  mutate(samp_count = get_count(n = 1000))
head(my_samples, n = 3)
# A tibble: 3 × 2
# Rowwise: 
  sample_id samp_count
      <int>      <int>
1         1        682
2         2        716
3         3        694

Tip

I don’t need n = 1000 because I set it as the default when I made my function.

Plotting the results

ggplot(my_samples,
       aes(x = samp_count)) +
  geom_histogram(aes(y = after_stat(density)), # for overlay
                 boundary = 697.5,     # why would I choose this?
                 binwidth = 5,         # somewhat arbitrary
                 color = "white",
                 fill = "gray") +
  geom_density(color = "#36454f",      # overlay density
               linewidth = 1,
               alpha = .5)

Plotting the results

Repeating with 2,500 samples

Sample size and number of samples

When we are doing simulations like this, it can be easy to confuse the sample size (1000) with the number of samples in our simulation (2500). They are not the same thing!

The sample size is the number of people we would survey “in the real world”.

The number of samples is how many times we want to run our simulated experiment.

How accurate are we?

We will do this formally later. But now we can quantify how accurately a sample proportion of 1000 people might estimate this population proportion by using the interquartile range. This is how wide the middle half of the data is.

my_many_samples |> pull(samp_count) |> quantile(c(.25, .75))
25% 75% 
691 710 
my_many_samples |> pull(samp_count) |> IQR()
[1] 19

Reminder

Remember: in real life we only get one of these samples.

Visualizing IQR

Sample size

Remember that we drew a sample of 1000 people to estimate our sample proportions. What if we had different sample sizes? Let’s compare the following:

  • \(n\) = 60
  • \(n\) = 250
  • \(n\) = 1000

Visualizing “accuracy”

Proportions

The x-axis is now proportion because we can no longer compare raw counts.

Comparing IQR

The interquartile ranges (i.e., widths of the middle half of the data) decrease a lot with sample size.

# A tibble: 3 × 2
  sample_size    IQR
  <chr>        <dbl>
1 n = 1000    0.0190
2 n = 250     0.0360
3 n = 60      0.0667

Warning

We will explore these issues more formally very soon using the concepts sampling distribution and standard error. For now, the goal is to understand how to use simulations to build qualitative intuition about sample size.

Thinking with real data: GSS

The General Social Survey is a repeated cross-sectional survey that has been fielded every year or other year since 1972. It is the “Hubble Telescope” of sociology!

Accessing the GSS in R

Install Kieran Healy’s gssr package using the code below. You only have to do this once.

# Install 'gssr' from 'ropensci' universe
install.packages('gssr', repos =
  c('https://kjhealy.r-universe.dev', 'https://cloud.r-project.org'))

# Also recommended: install 'gssrdoc' as well
install.packages('gssrdoc', repos =
  c('https://kjhealy.r-universe.dev', 'https://cloud.r-project.org'))

Getting the 2022 survey

library(gssr)

gss2022 <- gss_get_yr(year = 2022) |> # get 2022
  haven::zap_labels()                 # remove Stata value labels
Rows: 4,149
Columns: 1,185
$ year           <dbl> 2022, 2022, 2022, 2022, 2022, 2022, 2022, 202…
$ id             <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14…
$ wrkstat        <dbl> 1, 5, 1, 3, 8, 1, 2, 1, 1, 5, 7, 2, 1, 2, 7, …
$ hrs1           <dbl> 40, NA, 52, NA, NA, 50, 30, 40, 31, NA, NA, 3…
$ hrs2           <dbl> NA, NA, NA, 25, NA, NA, NA, NA, NA, NA, NA, N…
$ evwork         <dbl> NA, 1, NA, NA, 1, NA, NA, NA, NA, 1, 1, NA, N…
$ wrkslf         <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ occ10          <dbl> 430, 50, 4610, 4120, 7330, 4610, 1105, 2200, …
$ prestg10       <dbl> 39, 53, 48, 34, 38, 48, 61, 74, 31, 48, 39, 3…
$ prestg105plus  <dbl> 42, 73, 44, 29, 37, 44, 82, 94, 16, 50, 46, 2…
$ indus10        <dbl> 6290, 6695, 8290, 8660, 3390, 8180, 8090, 787…
$ marital        <dbl> 3, 1, 3, 5, 5, 5, 5, 1, 5, 5, 2, 5, 1, 5, 5, …
$ martype        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ divorce        <dbl> NA, 2, NA, NA, NA, NA, NA, 2, NA, NA, 2, NA, …
$ widowed        <dbl> 2, 1, 2, NA, NA, NA, NA, 2, NA, NA, NA, NA, 2…
$ spwrksta       <dbl> NA, 5, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA,…
$ sphrs1         <dbl> NA, NA, NA, NA, NA, NA, NA, 40, NA, NA, NA, N…
$ sphrs2         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spevwork       <dbl> NA, 1, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ cowrksta       <dbl> NA, NA, NA, NA, 7, 1, NA, NA, NA, NA, NA, NA,…
$ coevwork       <dbl> NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA, NA…
$ cohrs1         <dbl> NA, NA, NA, NA, NA, 37, NA, NA, NA, NA, NA, N…
$ cohrs2         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spwrkslf       <dbl> NA, 2, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA,…
$ sppres80       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spocc10        <dbl> NA, 2340, NA, NA, NA, NA, NA, 2200, NA, NA, N…
$ sppres10       <dbl> NA, 38, NA, NA, NA, NA, NA, 74, NA, NA, NA, N…
$ sppres105plus  <dbl> NA, 32, NA, NA, NA, NA, NA, 94, NA, NA, NA, N…
$ spind10        <dbl> NA, 6695, NA, NA, NA, NA, NA, 7870, NA, NA, N…
$ coocc10        <dbl> NA, NA, NA, NA, 3600, 4700, NA, NA, NA, NA, N…
$ coind10        <dbl> NA, NA, NA, NA, 8270, 5790, NA, NA, NA, NA, N…
$ pawrkslf       <dbl> 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, NA, 1, 2, 2, NA…
$ paocc10        <dbl> 800, 8900, 4220, 8965, 6260, 4850, 9620, 9130…
$ papres10       <dbl> 60, 35, 24, 35, 28, 45, 25, 35, 39, 25, NA, 3…
$ papres105plus  <dbl> 85, 29, 15, 28, 23, 55, 16, 29, 40, 16, NA, 4…
$ paind10        <dbl> 7280, 1370, 7860, 2990, 770, 1870, 4470, 4470…
$ mawrkslf       <dbl> 2, NA, 2, 2, 2, 2, NA, 2, 1, NA, 2, 1, 2, 2, …
$ maocc10        <dbl> 2010, NA, 4720, 3255, 5700, 5240, NA, 5140, 4…
$ mapres10       <dbl> 54, NA, 28, 64, 47, 31, NA, 40, 31, NA, 48, 3…
$ mapres105plus  <dbl> 68, NA, 16, 87, 55, 20, NA, 32, 16, NA, 44, 4…
$ maind10        <dbl> 9480, NA, 4970, 8190, 3490, 4970, NA, 580, 86…
$ sibs           <dbl> 1, 3, 1, 1, 2, 1, 3, 3, 4, 6, 15, 2, 4, 4, 4,…
$ childs         <dbl> 1, 2, 1, 0, 2, 0, 0, 0, 1, 4, 2, 0, 2, 2, 3, …
$ age            <dbl> 72, 80, 57, 23, 62, 27, 20, 47, 31, 72, 57, 2…
$ agekdbrn       <dbl> 27, 24, 27, NA, 21, NA, NA, NA, 28, 21, 21, N…
$ educ           <dbl> 16, 18, 12, 16, 14, 12, 12, 16, 12, 12, 13, 1…
$ paeduc         <dbl> 16, 12, 14, 14, 12, 12, 11, 6, 12, NA, NA, 8,…
$ maeduc         <dbl> 16, 12, 11, 18, 16, 14, 9, 18, 10, NA, NA, 18…
$ speduc         <dbl> NA, 16, NA, NA, NA, NA, NA, 16, NA, NA, NA, N…
$ coeduc         <dbl> NA, NA, NA, NA, 12, 12, NA, NA, NA, NA, NA, N…
$ codeg          <dbl> NA, NA, NA, NA, 1, 1, NA, NA, NA, NA, NA, NA,…
$ degree         <dbl> 3, 4, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, …
$ padeg          <dbl> 3, 1, 1, 1, 1, 1, 1, 0, 1, NA, NA, 0, 1, 1, N…
$ madeg          <dbl> 4, 1, 0, 4, 3, 2, 0, 4, 0, NA, NA, 4, 1, 1, 1…
$ spdeg          <dbl> NA, 3, NA, NA, NA, NA, NA, 4, NA, NA, NA, NA,…
$ major1         <dbl> 44, 9, NA, 44, NA, NA, NA, 16, NA, NA, NA, 25…
$ major2         <dbl> NA, NA, NA, 70, NA, NA, NA, NA, NA, NA, NA, 2…
$ dipged         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, …
$ sex            <dbl> 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, …
$ race           <dbl> 1, 1, 1, 1, 1, 1, 3, 1, 1, NA, 1, 1, 1, 1, 1,…
$ res16          <dbl> 5, 5, 3, 3, 3, 3, 6, 4, 3, 3, 4, 4, 3, 4, 5, …
$ reg16          <dbl> 2, 3, 1, 1, 1, 2, 2, 9, 5, 2, 2, 2, 2, 1, 1, …
$ mobile16       <dbl> 3, 3, 2, 1, 1, 1, 1, 3, 3, 1, 1, 2, 2, 1, 2, …
$ family16       <dbl> 1, 1, 3, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 5, …
$ famdif16       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mawrkgrw       <dbl> 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, NA,…
$ incom16        <dbl> 4, 2, 2, 4, 3, 1, 3, 2, 3, 2, 5, 4, 2, 2, 3, …
$ born           <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ parborn        <dbl> 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 1, 0, 3, …
$ granborn       <dbl> 4, NA, 1, 0, 2, 0, 4, 4, 0, NA, 0, 0, 2, 0, N…
$ hompop         <dbl> 1, 2, NA, 3, NA, 2, NA, NA, NA, NA, NA, NA, 6…
$ babies         <dbl> 0, 0, NA, 0, NA, 0, NA, NA, NA, NA, NA, NA, 0…
$ preteen        <dbl> 0, 0, NA, 0, NA, 0, NA, NA, NA, NA, NA, NA, 2…
$ teens          <dbl> 0, 0, NA, 0, NA, 0, NA, NA, NA, NA, NA, NA, 0…
$ adults         <dbl> 1, 2, 3, 3, 3, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, …
$ unrelat        <dbl> NA, 0, 1, 0, 0, 1, NA, 0, 0, NA, 0, NA, 0, 0,…
$ earnrs         <dbl> 1, 0, 1, 3, 1, 2, 1, 2, 1, 0, 1, 1, 4, 2, 2, …
$ income         <dbl> 12, NA, 12, 12, 12, 12, 12, 12, 11, 9, 12, 12…
$ rincome        <dbl> 12, NA, 12, 5, NA, 12, 12, 12, 10, NA, NA, 12…
$ income16       <dbl> 22, NA, 18, 22, 15, 19, 17, 26, 14, 9, 19, 16…
$ rincom16       <dbl> 22, NA, 18, 5, NA, 19, 17, 21, 11, NA, NA, 16…
$ region         <dbl> 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, …
$ xnorcsiz       <dbl> 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, …
$ srcbelt        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ size           <dbl> 10, 10, 10, 10, 10, 24, 24, 24, 24, 24, 24, 2…
$ partyid        <dbl> 0, 3, 5, 0, 3, 1, 2, 0, 2, 0, 3, 2, 7, 5, 3, …
$ vote16         <dbl> 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 2, 2, NA, 1,…
$ pres16         <dbl> 1, 1, 2, NA, 2, 1, NA, 1, 3, 3, 1, NA, NA, NA…
$ if16who        <dbl> NA, NA, NA, 1, NA, NA, 2, NA, NA, NA, NA, 4, …
$ polviews       <dbl> 2, 5, 4, 1, 5, 4, 3, 1, 3, 4, 4, NA, 4, 4, 6,…
$ natspac        <dbl> 2, 1, NA, 3, NA, 2, NA, NA, NA, NA, NA, NA, 2…
$ natenvir       <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natheal        <dbl> 1, 2, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natcity        <dbl> 2, 1, NA, 1, NA, 2, NA, NA, NA, NA, NA, NA, 1…
$ natcrime       <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natdrug        <dbl> 2, 2, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ nateduc        <dbl> 1, 2, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natrace        <dbl> 1, 3, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natarms        <dbl> 2, 2, NA, 3, NA, 3, NA, NA, NA, NA, NA, NA, 3…
$ nataid         <dbl> 2, 2, NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, 3…
$ natfare        <dbl> 2, 3, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ natroad        <dbl> 2, 1, 1, 2, 2, 1, 3, 1, NA, 1, 2, 1, 2, 2, 3,…
$ natsoc         <dbl> 1, 1, 2, 1, 1, 2, NA, 1, NA, 1, 1, NA, 1, 1, …
$ natmass        <dbl> 2, 2, 1, 1, 2, 1, 2, 1, NA, NA, 2, 1, 1, 2, 3…
$ natpark        <dbl> 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, …
$ natchld        <dbl> 3, 2, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ natsci         <dbl> 1, 2, 1, 3, 3, 2, 1, 2, 2, NA, 2, NA, 2, 1, 1…
$ natenrgy       <dbl> 2, 2, 3, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, …
$ natspacy       <dbl> NA, NA, 1, NA, 3, NA, 3, 3, NA, 3, 3, NA, NA,…
$ natenviy       <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, 1, 1, NA, …
$ nathealy       <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, 1, 1, 1, NA, N…
$ natcityy       <dbl> NA, NA, 3, NA, 3, NA, 3, 1, NA, 1, 3, 2, NA, …
$ natcrimy       <dbl> NA, NA, 1, NA, 1, NA, 3, 3, NA, 1, 2, 3, NA, …
$ natdrugy       <dbl> NA, NA, 1, NA, 3, NA, 1, 1, 1, 1, 1, 1, NA, N…
$ nateducy       <dbl> NA, NA, 1, NA, 2, NA, 1, 1, 1, 2, 1, 1, NA, N…
$ natracey       <dbl> NA, NA, 2, NA, 3, NA, 1, 1, NA, 1, 1, 1, NA, …
$ natarmsy       <dbl> NA, NA, 1, NA, 2, NA, 3, 3, 3, 1, 3, 3, NA, N…
$ nataidy        <dbl> NA, NA, 3, NA, 3, NA, 1, 2, 3, 3, 2, 3, NA, N…
$ natfarey       <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, 1, 1, 1, NA, N…
$ eqwlth         <dbl> 1, NA, 5, NA, 1, 1, 3, 1, NA, 7, 4, 1, 2, 4, …
$ tax            <dbl> 1, 1, 1, 1, 1, 1, NA, 2, 1, NA, NA, 2, NA, 3,…
$ spkath         <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ colath         <dbl> 4, 4, 5, 4, 4, 4, 4, 4, 5, NA, NA, 4, NA, 5, …
$ libath         <dbl> 2, 2, NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, N…
$ spkrac         <dbl> 1, NA, NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, …
$ colrac         <dbl> 5, 4, 5, 5, 4, 5, 5, 5, 5, NA, NA, 5, NA, 5, …
$ librac         <dbl> 2, 2, NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ spkcom         <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ colcom         <dbl> 5, 5, NA, 5, NA, 5, NA, NA, NA, NA, NA, NA, N…
$ libcom         <dbl> 2, 2, NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, N…
$ spkmslm        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ colmslm        <dbl> 5, 5, 5, 4, 4, 5, 5, 4, 5, NA, NA, 5, NA, 5, …
$ libmslm        <dbl> 2, 2, NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ cappun         <dbl> 2, 1, 1, 2, 2, 2, 2, 2, 1, NA, 2, 2, 1, 1, 1,…
$ gunlaw         <dbl> 1, 2, 1, 1, 2, 1, 1, 1, NA, NA, NA, NA, NA, 1…
$ courts         <dbl> NA, NA, NA, NA, NA, NA, 3, NA, 2, 2, NA, NA, …
$ grass          <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, 1, NA, 1, …
$ relig          <dbl> 4, 2, 5, 4, 2, 4, 4, 4, 4, 5, 4, 4, 10, 2, 2,…
$ denom          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ other          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ jew            <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fund           <dbl> 3, 2, NA, 3, 2, 3, 3, 3, 3, NA, 3, 3, 3, 2, 2…
$ attend         <dbl> 2, 2, 0, 4, 2, 0, 1, 1, 0, 7, 0, 1, 2, 1, 4, …
$ reliten        <dbl> NA, NA, NA, NA, NA, NA, 4, NA, 4, 1, NA, 4, 2…
$ postlife       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 2,…
$ pray           <dbl> 6, 5, 5, 4, 4, 6, 4, 6, 3, 1, 2, 5, 5, 5, 1, …
$ popespks       <dbl> NA, 4, NA, NA, 2, NA, NA, NA, NA, NA, NA, NA,…
$ relig16        <dbl> 4, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, …
$ denom16        <dbl> NA, NA, 70, NA, NA, NA, 60, NA, NA, 18, 28, N…
$ oth16          <dbl> NA, NA, NA, NA, NA, NA, 77, NA, NA, NA, NA, N…
$ jew16          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fund16         <dbl> 3, 2, 2, 2, 2, 2, 1, 2, 2, 1, 3, 2, 2, 2, 2, …
$ sprel          <dbl> NA, 2, NA, NA, NA, NA, NA, 4, NA, NA, NA, NA,…
$ spden          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spother        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spjew          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spfund         <dbl> NA, 2, NA, NA, NA, NA, NA, 3, NA, NA, NA, NA,…
$ corel          <dbl> NA, NA, NA, NA, 2, 4, NA, NA, NA, NA, NA, NA,…
$ coden          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ coother        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ cojew          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ cofund         <dbl> NA, NA, NA, NA, 2, 3, NA, NA, NA, NA, NA, NA,…
$ prayer         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 2, NA, NA,…
$ bible          <dbl> NA, NA, NA, NA, NA, NA, 3, NA, 3, 1, NA, 3, 2…
$ racopen        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ raclive        <dbl> 1, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,…
$ affrmact       <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 4, 3, 2, NA, 2,…
$ wrkwayup       <dbl> NA, 1, NA, 4, NA, NA, NA, NA, 4, 2, 3, NA, 5,…
$ happy          <dbl> 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, …
$ hapmar         <dbl> NA, 2, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA,…
$ hapcohab       <dbl> NA, NA, NA, NA, 2, 1, NA, NA, NA, NA, NA, NA,…
$ health         <dbl> 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 2, 3, 3, 2, 1, …
$ life           <dbl> 2, 2, 2, 2, 2, 1, 2, 2, 1, NA, NA, 2, NA, 2, …
$ helpful        <dbl> NA, NA, NA, NA, NA, NA, 3, NA, NA, 1, NA, 2, …
$ fair           <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, 2, NA, 1, …
$ trust          <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, 2, NA, 2, …
$ confinan       <dbl> 2, NA, 3, NA, 2, 3, 2, 3, NA, 1, 3, 3, 2, 2, …
$ conbus         <dbl> 3, NA, 2, NA, 2, 3, 2, 3, NA, 2, 2, 3, 2, 2, …
$ conclerg       <dbl> 3, NA, 1, NA, 2, 3, NA, 2, NA, 1, 3, 2, 2, 2,…
$ coneduc        <dbl> 3, NA, 3, NA, 2, 1, 2, 2, NA, 1, 1, 2, 2, 2, …
$ confed         <dbl> 1, NA, 3, NA, 3, 3, 2, 2, NA, 2, 3, 3, 2, 2, …
$ conlabor       <dbl> 2, NA, 2, NA, 2, 3, 3, 1, NA, 2, 2, 2, 3, 2, …
$ conpress       <dbl> 2, NA, 3, NA, 3, 3, 3, 1, NA, 2, 3, 2, 3, 2, …
$ conmedic       <dbl> 1, NA, 2, NA, 2, 3, 2, 1, NA, 2, 1, 2, 2, 2, …
$ contv          <dbl> 2, NA, 3, NA, 2, 3, 2, 2, NA, 1, 2, 2, 3, 2, …
$ conjudge       <dbl> 3, NA, 1, NA, 2, 3, NA, 2, NA, 2, 3, 3, 3, 2,…
$ consci         <dbl> 1, NA, 2, NA, 1, 3, 1, 1, NA, NA, 1, 2, 2, 2,…
$ conlegis       <dbl> 3, NA, 3, NA, 3, 3, 2, 2, NA, 3, 3, 3, 3, 2, …
$ conarmy        <dbl> 2, NA, 2, NA, 1, 3, 2, 2, NA, 1, 1, 3, 2, 1, …
$ obey           <dbl> 5, NA, 4, NA, 4, 4, 5, 5, NA, 4, 5, NA, NA, 3…
$ popular        <dbl> 4, NA, 5, NA, 5, 5, 4, 4, NA, 5, 4, NA, NA, 5…
$ thnkself       <dbl> 1, NA, 1, NA, 2, 1, 1, 1, NA, 2, 1, NA, NA, 4…
$ workhard       <dbl> 3, NA, 2, NA, 1, 2, 2, 3, NA, 1, 3, NA, NA, 2…
$ helpoth        <dbl> 2, NA, 3, NA, 3, 3, 3, 2, NA, 3, 2, NA, NA, 1…
$ socrel         <dbl> NA, 5, NA, 3, NA, NA, NA, NA, 2, 5, 2, NA, 2,…
$ socommun       <dbl> NA, 6, NA, 3, NA, NA, NA, NA, 3, 7, 4, NA, 5,…
$ socfrend       <dbl> NA, 5, NA, 3, NA, NA, NA, NA, 7, 7, 2, NA, 5,…
$ socbar         <dbl> NA, 5, NA, 3, NA, NA, NA, NA, 6, 7, 5, NA, 5,…
$ aged           <dbl> NA, NA, NA, NA, NA, NA, 3, NA, NA, 2, NA, 1, …
$ weekswrk       <dbl> 52, 0, 47, 40, 0, 50, 52, 52, 32, 0, 0, 51, 5…
$ partfull       <dbl> 1, NA, 1, 1, NA, 1, 1, 1, 2, NA, NA, 2, 1, 2,…
$ joblose        <dbl> NA, NA, NA, 4, NA, NA, NA, NA, 4, NA, NA, NA,…
$ jobfind        <dbl> NA, NA, NA, 1, NA, NA, NA, NA, 2, NA, NA, NA,…
$ satjob         <dbl> 3, NA, 3, 3, NA, 2, 3, 2, 1, NA, 2, 1, 1, 3, …
$ richwork       <dbl> 2, NA, 1, 1, NA, 1, 1, 2, 1, NA, NA, 1, NA, 1…
$ class          <dbl> 3, 3, 2, 3, 3, 1, 1, 4, 2, 2, 2, 3, 2, 3, 2, …
$ rank           <dbl> NA, 4, NA, 4, NA, NA, NA, NA, 5, NA, NA, NA, …
$ satfin         <dbl> 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, …
$ finalter       <dbl> 3, 2, 2, 3, 2, 3, 1, 2, 3, 3, 2, 1, 3, 2, 2, …
$ finrela        <dbl> 3, 3, 3, 4, 2, 3, 2, 5, 3, 3, 2, 4, 3, 2, 1, …
$ wksub          <dbl> 1, NA, 1, 1, NA, 1, 1, 1, 1, NA, NA, 1, 1, 2,…
$ wksubs         <dbl> 3, NA, 3, 3, NA, 3, 3, 3, 4, NA, NA, 4, 3, NA…
$ wksub1         <dbl> 1, NA, 1, 1, NA, 1, 1, 1, 1, NA, NA, 1, 1, 2,…
$ wksubs1        <dbl> 3, NA, 3, 3, NA, 3, 3, 3, 4, NA, NA, 4, 3, NA…
$ wksup          <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 1, NA, NA, 2, 1, 2,…
$ wksups         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 4, NA, NA, NA…
$ wksup1         <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 1, NA, NA, 2, 1, 2,…
$ wksups1        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 4, NA, NA, NA…
$ unemp          <dbl> 2, NA, 2, NA, 2, 2, 2, 2, NA, 2, 2, 1, 1, 2, …
$ union          <dbl> 4, NA, 1, NA, 4, 4, NA, 4, NA, 1, 4, 4, 4, 4,…
$ union1         <dbl> 4, NA, 1, NA, 4, 4, NA, 4, NA, 1, 4, 4, 4, 4,…
$ getahead       <dbl> NA, NA, NA, NA, NA, NA, 2, NA, 2, NA, NA, 2, …
$ parsol         <dbl> 4, NA, 3, NA, 4, 5, 1, 1, NA, 1, 1, 2, 4, 3, …
$ kidssol        <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, 1, NA, NA,…
$ fepol          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, 2, NA, NA,…
$ abdefect       <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ abnomore       <dbl> NA, NA, 1, NA, 2, NA, 1, 1, 1, NA, NA, 1, NA,…
$ abhlth         <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ abpoor         <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ abrape         <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ absingle       <dbl> NA, NA, 1, NA, 2, NA, 1, 1, 1, NA, NA, 1, NA,…
$ abany          <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ chldidel       <dbl> NA, 3, NA, 8, NA, NA, NA, NA, 8, 8, 8, NA, 2,…
$ pillok         <dbl> NA, 2, NA, 2, NA, NA, NA, NA, 3, 2, 1, NA, 1,…
$ sexeduc        <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 2, 1, NA, 1,…
$ divlaw         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA, NA…
$ premarsx       <dbl> NA, 4, NA, 4, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ teensex        <dbl> NA, 1, NA, 3, NA, NA, NA, NA, 1, 4, 3, NA, 3,…
$ xmarsex        <dbl> 1, 2, 2, 3, 1, 3, 3, 1, 2, NA, NA, 3, NA, 1, …
$ homosex        <dbl> 4, 3, 4, 4, 1, 4, 4, 4, 4, NA, NA, 4, NA, 4, …
$ pornlaw        <dbl> 2, NA, 2, NA, 1, 2, 2, 2, NA, 2, 2, 2, 2, 2, …
$ xmovie         <dbl> 2, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ spanking       <dbl> NA, 3, NA, 2, NA, NA, NA, NA, 3, 2, 3, NA, 3,…
$ letdie1        <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ suicide1       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 1, 1, NA, …
$ suicide2       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, 2, 2, NA, …
$ suicide3       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, 2, 2, NA, …
$ suicide4       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, 2, 2, NA, …
$ polhitok       <dbl> 1, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ polabuse       <dbl> 2, NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, NA,…
$ polmurdr       <dbl> 2, NA, 2, NA, 2, 2, 2, 2, NA, 1, 2, 2, 2, 2, …
$ polescap       <dbl> 1, NA, 1, NA, 1, 1, 1, 2, NA, 2, 1, NA, 2, 2,…
$ polattak       <dbl> 1, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ fear           <dbl> 2, 1, 2, 2, 2, 1, 1, 2, 1, NA, NA, 1, NA, 2, …
$ owngun         <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, NA, NA, 2, NA, 2, …
$ pistol         <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, NA, NA, 2, NA, 2, …
$ shotgun        <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, NA, NA, 2, NA, 2, …
$ rifle          <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, NA, NA, 2, NA, 2, …
$ rowngun        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ hunt           <dbl> 4, 4, 4, 4, 4, 4, 4, 4, 4, NA, NA, 4, NA, 4, …
$ hunt1          <dbl> 4, 4, 4, 4, 4, 4, 4, 4, 4, NA, NA, 4, NA, 4, …
$ news           <dbl> NA, 1, NA, 5, NA, NA, NA, NA, 4, 5, 4, NA, 2,…
$ tvhours        <dbl> NA, 3, NA, 1, NA, NA, NA, NA, 0, 19, 2, NA, 2…
$ phone          <dbl> 1, 1, 6, 6, 6, 6, 6, 2, 6, 6, 1, 2, 6, 6, 1, …
$ coop           <dbl> 1, NA, NA, NA, NA, NA, 1, NA, 1, 1, NA, 1, 1,…
$ comprend       <dbl> 1, NA, NA, NA, NA, NA, 1, NA, 1, 1, NA, 2, 1,…
$ form           <dbl> 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, …
$ fechld         <dbl> NA, 3, NA, 2, NA, NA, NA, NA, 2, 1, 2, NA, 1,…
$ fepresch       <dbl> NA, 2, NA, 3, NA, NA, NA, NA, 3, 3, 3, NA, 4,…
$ fefam          <dbl> NA, 4, NA, 4, NA, NA, NA, NA, 4, 3, 4, NA, 4,…
$ racdif1        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, 1, NA,…
$ racdif2        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, NA, 2, NA,…
$ racdif3        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 2, 1, NA, …
$ racdif4        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, 2, NA,…
$ helppoor       <dbl> 2, NA, 4, NA, 1, 1, 1, 1, NA, 3, 3, 1, 2, 3, …
$ helpnot        <dbl> 2, NA, 5, NA, 1, 1, 2, 1, NA, 3, 3, 1, 4, 3, …
$ helpsick       <dbl> 1, NA, 4, NA, 1, 1, 2, 1, NA, 2, 1, 1, 3, 3, …
$ helpblk        <dbl> 2, NA, 4, NA, 5, 1, NA, 1, NA, 2, 3, 1, 2, 3,…
$ god            <dbl> 1, NA, 6, NA, 5, 1, 3, 2, NA, 6, 3, 2, 5, 3, …
$ reborn         <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, …
$ savesoul       <dbl> 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ wlthwhts       <dbl> NA, 4, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ wlthblks       <dbl> NA, 5, NA, 6, NA, NA, NA, NA, NA, NA, NA, NA,…
$ wlthhsps       <dbl> NA, 5, NA, 4, NA, NA, NA, NA, NA, NA, NA, NA,…
$ workwhts       <dbl> NA, 3, NA, 4, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ workblks       <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ workhsps       <dbl> NA, 3, NA, 2, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ intlwhts       <dbl> NA, 5, NA, 4, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ intlblks       <dbl> NA, 3, NA, 4, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ intlhsps       <dbl> NA, 3, NA, 4, NA, NA, NA, NA, 4, 4, 4, NA, 4,…
$ liveblks       <dbl> NA, 5, NA, 1, NA, NA, NA, NA, 3, 3, 1, NA, 3,…
$ marblk         <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 3, 3, 1, NA, 3,…
$ marasian       <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, 3, 1, NA, 3,…
$ marhisp        <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 3, 3, 1, NA, 3,…
$ marwht         <dbl> NA, 2, NA, 3, NA, NA, NA, NA, 3, 3, 1, NA, 3,…
$ racwork        <dbl> NA, NA, 3, 3, NA, 3, 3, 2, 1, NA, NA, 2, NA, …
$ discaff        <dbl> 2, 2, 2, 3, 3, 3, 2, 3, NA, 3, 2, 3, 3, 3, 1,…
$ yousup         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 4, NA, NA, NA…
$ spwksup        <dbl> NA, NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA…
$ fejobaff       <dbl> NA, 3, NA, 4, NA, NA, NA, NA, NA, NA, NA, NA,…
$ discaffm       <dbl> NA, 2, NA, 3, NA, NA, NA, NA, NA, NA, NA, NA,…
$ discaffw       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, 1, NA, NA,…
$ fehire         <dbl> NA, 3, NA, 1, NA, NA, NA, NA, 3, 1, 1, NA, 2,…
$ relpersn       <dbl> 4, 3, 3, 3, 2, 4, 3, 4, 4, 2, 3, 4, 3, 4, 3, …
$ sprtprsn       <dbl> 4, 2, 2, 3, 3, 3, 2, 3, 1, 1, 1, 3, 2, 4, 1, …
$ othlang        <dbl> 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, …
$ spklang        <dbl> NA, 3, NA, NA, NA, NA, 2, 3, NA, NA, NA, 3, N…
$ betrlang       <dbl> NA, 1, NA, NA, NA, NA, 1, 1, NA, NA, NA, 1, N…
$ letinhsp       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ letinasn       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ compuse        <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 2, 2, 1, NA, 1,…
$ webmob         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 1, NA, NA,…
$ emailmin       <dbl> NA, 0, NA, 30, NA, NA, NA, NA, 0, 0, 15, NA, …
$ emailhr        <dbl> NA, 7, NA, 5, NA, NA, NA, NA, 1, 0, 0, NA, 6,…
$ usewww         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 2, NA, NA…
$ wwwhr          <dbl> NA, 1, NA, 5, NA, NA, NA, NA, 14, 0, 1, NA, 3…
$ wwwmin         <dbl> NA, 0, NA, 0, NA, NA, NA, NA, 0, 0, 0, NA, 0,…
$ huclean        <dbl> 2, NA, NA, NA, NA, NA, 6, NA, 2, 1, NA, 6, 6,…
$ wrktype        <dbl> 5, NA, 5, 5, NA, 5, 5, 5, 5, NA, NA, 5, 5, 5,…
$ yearsjob       <dbl> 18.00, NA, 6.00, 5.00, NA, 6.00, 0.75, 10.00,…
$ waypaid        <dbl> 1, NA, 2, 2, NA, 2, 2, 1, 2, NA, NA, 2, 2, 2,…
$ wrksched       <dbl> 1, NA, 2, 1, NA, 3, 2, 5, 3, NA, NA, 1, 6, 1,…
$ moredays       <dbl> 5, NA, 5, 0, NA, 8, 2, 7, 5, NA, NA, 2, 2, 0,…
$ mustwork       <dbl> 2, NA, 2, 1, NA, 1, 1, 2, 2, NA, NA, 2, 2, 2,…
$ wrkhome        <dbl> 6, NA, 1, 1, NA, 1, 1, 5, 4, NA, NA, 1, 1, 1,…
$ whywkhme       <dbl> 1, NA, NA, NA, NA, NA, NA, 1, 1, NA, NA, NA, …
$ famwkoff       <dbl> 1, NA, 3, 4, NA, 3, 3, 2, 3, NA, NA, 2, 2, 1,…
$ wkvsfam        <dbl> 2, NA, 3, 1, NA, 1, 1, 3, 2, NA, NA, 4, 3, 4,…
$ famvswk        <dbl> 3, NA, 3, 4, NA, 2, 3, 3, 1, NA, NA, 3, 3, 4,…
$ hrsrelax       <dbl> 4, NA, 5, 10, NA, 4, 4, 4, 2, NA, NA, 5, 6, 1…
$ secondwk       <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 1, NA, NA, 2, 2, 2,…
$ learnnew       <dbl> 2, NA, 2, 4, NA, 1, 2, 1, 2, NA, NA, 1, 2, 2,…
$ workfast       <dbl> 3, NA, 3, 1, NA, 1, 2, 3, 1, NA, NA, 2, 2, 2,…
$ workdiff       <dbl> 1, NA, 1, 4, NA, 1, 3, 1, 1, NA, NA, 1, 2, 2,…
$ overwork       <dbl> 2, NA, 3, 2, NA, 1, 3, 2, 3, NA, NA, 3, 3, 2,…
$ knowwhat       <dbl> 1, NA, 1, 1, NA, 1, 2, 2, 2, NA, NA, 2, 2, 2,…
$ myskills       <dbl> 2, NA, 2, 4, NA, 1, 3, 1, 1, NA, NA, 1, 1, 2,…
$ respect        <dbl> 1, NA, 1, 2, NA, 1, NA, 1, 2, NA, NA, 1, 2, 3…
$ trustman       <dbl> 1, NA, 2, 2, NA, 1, 3, 2, 1, NA, NA, 1, 1, 3,…
$ safetywk       <dbl> 1, NA, 2, 3, NA, 1, 4, 2, 1, NA, NA, 1, 2, 2,…
$ safefrst       <dbl> 1, NA, 2, 1, NA, 1, 3, 2, 1, NA, NA, 2, 1, 2,…
$ teamsafe       <dbl> 1, NA, 2, 2, NA, 1, 3, 2, 1, NA, NA, 1, 1, 2,…
$ safehlth       <dbl> 1, NA, 2, 1, NA, 1, 2, 1, 1, NA, NA, 2, 1, 2,…
$ proudemp       <dbl> 2, NA, 2, 2, NA, 1, 3, 2, 1, NA, NA, 2, 2, 2,…
$ prodctiv       <dbl> 2, NA, 2, 3, NA, 1, 3, 2, 2, NA, NA, 2, 3, 2,…
$ wksmooth       <dbl> 2, NA, 2, 4, NA, 1, 3, 2, 2, NA, NA, 2, 2, 2,…
$ trdunion       <dbl> 2, NA, 2, 2, NA, 1, NA, 1, NA, NA, NA, 2, 3, …
$ partteam       <dbl> 1, NA, 1, 1, NA, 1, 1, 1, 1, NA, NA, 1, 1, 1,…
$ wkdecide       <dbl> 3, NA, 2, 4, NA, 1, 1, 2, 2, NA, NA, 1, 2, 4,…
$ toofewwk       <dbl> 2, NA, 2, 1, NA, 1, 1, 1, 1, NA, NA, 3, 2, 4,…
$ promteok       <dbl> 3, NA, 3, 2, NA, 1, 3, 2, 3, NA, NA, 3, 2, 4,…
$ opdevel        <dbl> 2, NA, 3, 4, NA, 1, 3, 1, 2, NA, NA, 1, 2, 4,…
$ hlpequip       <dbl> 1, NA, 1, 3, NA, 1, 2, 1, 1, NA, NA, 1, 2, 2,…
$ haveinfo       <dbl> 1, NA, 1, 1, NA, 1, 2, 1, 1, NA, NA, 1, 2, 2,…
$ wkfreedm       <dbl> 1, NA, 2, 4, NA, 1, 2, 1, 1, NA, NA, 2, 3, 2,…
$ fringeok       <dbl> 1, NA, 3, 3, NA, 1, 2, 1, 4, NA, NA, 2, 2, 2,…
$ supcares       <dbl> 1, NA, 1, 4, NA, 1, 1, 2, 1, NA, NA, 1, 1, 1,…
$ condemnd       <dbl> 3, NA, 2, 2, NA, 1, 2, 2, 2, NA, NA, 2, 3, 1,…
$ promtefr       <dbl> 1, NA, 2, 3, NA, 2, 3, 2, 1, NA, NA, 1, 2, 2,…
$ cowrkint       <dbl> 2, NA, 2, 1, NA, 1, 2, 2, 1, NA, NA, 1, 1, 2,…
$ jobsecok       <dbl> 1, NA, 1, 2, NA, 1, 3, 1, 1, NA, NA, 1, 2, 2,…
$ suphelp        <dbl> 1, NA, 1, 4, NA, 1, 2, 2, 1, NA, NA, 1, 1, 2,…
$ wrktime        <dbl> 3, NA, 2, 3, NA, 1, 2, 2, 2, NA, NA, 1, 3, 1,…
$ cowrkhlp       <dbl> 1, NA, 1, 1, NA, 1, 1, 2, 2, NA, NA, 2, 2, 1,…
$ manvsemp       <dbl> 1, NA, 2, 3, NA, 3, 3, 3, 1, NA, NA, 2, 1, 3,…
$ hvylift        <dbl> 2, NA, 1, 1, NA, 1, 1, 2, 1, NA, NA, 1, 1, 2,…
$ handmove       <dbl> 1, NA, 2, 1, NA, 1, 1, 2, 2, NA, NA, 1, 2, 2,…
$ wkpraise       <dbl> 1, NA, 1, 1, NA, 2, 3, 2, 2, NA, NA, 1, 1, 2,…
$ fairearn       <dbl> 3, NA, 3, 3, NA, 3, 1, 2, 3, NA, NA, 2, 2, 3,…
$ rincblls       <dbl> 1, NA, 2, 2, NA, 2, 2, 1, 2, NA, NA, 1, 2, 2,…
$ laidoff        <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ jobfind1       <dbl> 3, NA, 1, 3, NA, 2, 1, 2, 2, NA, NA, 2, 2, 3,…
$ trynewjb       <dbl> 3, NA, 3, 1, NA, 2, 2, 3, 3, NA, NA, 3, 3, 3,…
$ wkageism       <dbl> 2, NA, 2, 2, NA, 2, 1, 2, 2, NA, NA, 1, 2, 2,…
$ wkracism       <dbl> 2, NA, 2, 2, NA, 2, 1, 2, 2, NA, NA, 2, 2, 2,…
$ wksexism       <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ wkharsex       <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ wkharoth       <dbl> 2, NA, 2, 2, NA, 2, 1, 2, 1, NA, NA, 2, 1, 2,…
$ health1        <dbl> 3, NA, 2, 2, NA, 3, 3, 2, 2, NA, NA, 4, 4, 3,…
$ physhlth       <dbl> 30, NA, 0, 4, NA, 0, 2, 0, 5, NA, NA, 5, 15, …
$ mntlhlth       <dbl> 15, NA, 0, 10, NA, NA, 14, 0, 5, NA, NA, 7, 1…
$ hlthdays       <dbl> 0, NA, 0, 0, NA, 0, 1, 0, 0, NA, NA, 2, 5, 5,…
$ usedup         <dbl> 4, NA, 4, 2, NA, 3, 2, 3, 3, NA, NA, 4, 2, 3,…
$ backpain       <dbl> 2, NA, 1, 2, NA, 2, 2, 2, 2, NA, NA, 2, 1, 2,…
$ painarms       <dbl> 1, NA, 2, 2, NA, 2, 1, 2, 2, NA, NA, 2, 1, 2,…
$ hurtatwk       <dbl> 0, NA, 0, 0, NA, 0, 1, 0, 0, NA, NA, 0, 0, 0,…
$ spvtrfair      <dbl> 1, NA, 1, 2, NA, 3, 2, 1, 1, NA, NA, 1, 1, NA…
$ strredpg       <dbl> 2, NA, 2, 2, NA, 2, 2, 1, 2, NA, NA, 2, 1, 1,…
$ phyeffrt       <dbl> 4, NA, 3, 2, NA, 3, 2, 4, 3, NA, NA, 4, 3, 4,…
$ slpprblm       <dbl> 1, NA, 3, 2, NA, 2, 1, 3, 3, NA, NA, 3, 2, 4,…
$ satjob1        <dbl> 2, NA, 2, 3, NA, 3, 3, NA, 1, NA, NA, 1, 1, 3…
$ knowschd       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ usetech        <dbl> 100, NA, 5, 0, NA, 75, NA, 80, 10, NA, NA, 70…
$ stress12       <dbl> NA, NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA…
$ hyperten       <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ arthrtis       <dbl> 1, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ diabetes       <dbl> 2, NA, 2, 2, NA, 2, 2, 2, 2, NA, NA, 2, 2, 2,…
$ depress        <dbl> 1, NA, 1, 2, NA, 2, 1, 2, 2, NA, NA, 2, 1, 2,…
$ weight         <dbl> 172, NA, 128, 155, NA, 200, 175, 152, 125, NA…
$ height         <dbl> 64, NA, 63, 63, NA, 72, 63, 68, 64, NA, NA, 6…
$ ntwkhard       <dbl> 5, NA, 0, 2, NA, 0, 25, 15, 0, NA, NA, 0, 15,…
$ misswork       <dbl> 0, NA, 0, 2, NA, 0, 2, 0, 0, NA, NA, 0, 0, 0,…
$ lifenow        <dbl> 7, NA, 5, 8, NA, 9, 7, 8, 10, NA, NA, 8, 8, 5…
$ lifein5        <dbl> 7, NA, 8, 6, NA, NA, 9, 8, NA, NA, NA, NA, 9,…
$ disrspct       <dbl> 5, 4, 4, 4, 6, 5, 2, 4, 6, NA, NA, 3, NA, 1, …
$ poorserv       <dbl> 6, 5, 4, 5, 6, 5, 2, 5, 6, NA, NA, 6, NA, 3, …
$ notsmart       <dbl> 5, 5, 4, 5, 6, 6, 3, 6, 6, NA, NA, 3, NA, 3, …
$ afraidof       <dbl> 6, 4, 5, 6, 6, 6, 3, 5, 6, NA, NA, 4, NA, 6, …
$ threaten       <dbl> 5, 5, 5, 2, 6, 6, 6, 6, 6, NA, NA, 4, NA, 6, …
$ abmoral        <dbl> 2, NA, NA, 2, 3, NA, NA, NA, NA, NA, 2, NA, N…
$ abhelp1        <dbl> 1, NA, NA, 1, 1, NA, NA, NA, NA, NA, 1, NA, N…
$ abhelp2        <dbl> 1, NA, NA, 2, 2, NA, NA, NA, NA, NA, 1, NA, N…
$ abhelp3        <dbl> 1, NA, NA, 2, 2, NA, NA, NA, NA, NA, 1, NA, N…
$ abhelp4        <dbl> 1, NA, NA, 1, 1, NA, NA, NA, NA, NA, 1, NA, N…
$ workfor1       <dbl> 1, NA, 2, NA, NA, 3, 1, 2, NA, NA, NA, 1, 1, …
$ ownstock       <dbl> 2, NA, NA, NA, NA, NA, 3, NA, NA, NA, NA, 2, …
$ stockops       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ extrapay       <dbl> 2, NA, 2, NA, NA, 2, 1, 2, NA, NA, NA, 1, 1, …
$ compperf       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 1,…
$ deptperf       <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA, 2,…
$ indperf        <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 1,…
$ extrayr        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2…
$ numemps        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ wrkslffam      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ nextgen        <dbl> 1, NA, NA, 1, 3, NA, NA, NA, NA, NA, 1, NA, N…
$ toofast        <dbl> 3, NA, NA, 1, 2, NA, NA, NA, NA, NA, 3, NA, N…
$ advfront       <dbl> 2, NA, NA, 2, 2, NA, NA, NA, NA, NA, 1, NA, N…
$ scientgo       <dbl> 1, NA, NA, 2, 2, NA, NA, NA, NA, NA, 1, NA, N…
$ scienthe       <dbl> 1, NA, NA, 1, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ scientbe       <dbl> 1, NA, NA, 2, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ buyvalue       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ compwage       <dbl> 3, NA, 4, NA, NA, 3, 2, 2, NA, NA, NA, 4, 3, …
$ empinput       <dbl> 2, NA, 2, NA, NA, 2, 2, 2, NA, NA, NA, 1, 2, …
$ slfmangd       <dbl> 1, NA, 2, NA, NA, 2, 2, 1, NA, NA, NA, 1, 1, …
$ emptrain       <dbl> 2, NA, 2, NA, NA, 1, 1, 2, NA, NA, NA, 1, 1, …
$ wealth         <dbl> 9, NA, 2, NA, NA, 4, 1, 8, NA, NA, NA, 2, 3, …
$ esop           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ defpensn       <dbl> 2, NA, 2, NA, NA, 1, 2, 2, NA, NA, NA, 2, 2, …
$ ratetone       <dbl> 1, NA, NA, NA, NA, NA, 2, NA, 1, 3, NA, 2, 1,…
$ posslq         <dbl> 4, 1, NA, 4, NA, 2, NA, NA, NA, NA, NA, NA, 1…
$ posslqy        <dbl> NA, NA, 4, NA, 2, NA, 4, 1, 4, 4, 4, 4, NA, N…
$ marcohab       <dbl> 3, 1, 3, 3, 2, 2, 3, 1, 3, 3, 3, 3, 1, 3, 2, …
$ healthissp     <dbl> 3, NA, 2, NA, 4, 2, 3, 2, NA, NA, NA, 4, NA, …
$ endsmeet       <dbl> NA, 3, NA, 5, NA, NA, NA, NA, 2, NA, NA, NA, …
$ goodlife       <dbl> 4, NA, 4, NA, 4, 4, 2, 4, NA, 2, 4, 3, 4, 3, …
$ famsuffr       <dbl> NA, 4, NA, 5, NA, NA, NA, NA, NA, NA, NA, NA,…
$ homekid        <dbl> NA, 4, NA, 5, NA, NA, NA, NA, 3, NA, NA, NA, …
$ housewrk       <dbl> NA, 5, NA, 3, NA, NA, NA, NA, 2, NA, NA, NA, …
$ wrkbaby        <dbl> NA, 3, NA, NA, NA, NA, NA, NA, 3, NA, NA, NA,…
$ wrksch         <dbl> NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ marlegit       <dbl> NA, 2, NA, 4, NA, NA, NA, NA, 4, NA, NA, NA, …
$ marmakid       <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 2, NA, NA, NA, …
$ marpakid       <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 2, NA, NA, NA, …
$ marhomo        <dbl> 1, 2, 1, 1, 4, 1, 2, 1, 1, NA, NA, 1, NA, 1, …
$ numkids        <dbl> NA, 2, NA, 3, NA, NA, NA, NA, NA, NA, NA, NA,…
$ kidnofre       <dbl> NA, 3, NA, 1, NA, NA, NA, NA, 4, NA, NA, NA, …
$ hubbywk1       <dbl> NA, 4, NA, 5, NA, NA, NA, NA, 4, NA, NA, NA, …
$ meovrwrk       <dbl> NA, 1, NA, 2, NA, NA, NA, NA, 3, 3, 3, NA, 4,…
$ cohabok        <dbl> NA, 2, NA, 1, NA, NA, NA, NA, 2, NA, NA, NA, …
$ laundry1       <dbl> NA, 3, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ caresik1       <dbl> NA, 3, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ shop1          <dbl> NA, 3, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ cooking1       <dbl> NA, 4, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ rhhwork        <dbl> NA, 20, NA, 8, NA, NA, NA, NA, 10, NA, NA, NA…
$ sphhwork       <dbl> NA, 20, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ happy7         <dbl> 4, 3, 5, 3, 4, 3, 3, 3, 2, NA, NA, 3, NA, 2, …
$ ssfchild       <dbl> NA, 4, NA, 2, NA, NA, NA, NA, 2, NA, NA, NA, …
$ ssmchild       <dbl> NA, 4, NA, 2, NA, NA, NA, NA, 2, NA, NA, NA, …
$ kidsocst       <dbl> NA, 2, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ paidlv         <dbl> NA, 0, NA, 6, NA, NA, NA, NA, 6, NA, NA, NA, …
$ paidlvdv       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 2, NA, NA, NA…
$ famwkbst       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 4, NA, NA, NA…
$ famwklst       <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 6, NA, NA, NA, …
$ careprov       <dbl> NA, 1, NA, 5, NA, NA, NA, NA, 1, NA, NA, NA, …
$ carecost       <dbl> NA, 1, NA, 3, NA, NA, NA, NA, NA, NA, NA, NA,…
$ eldhelp        <dbl> NA, 4, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ eldcost        <dbl> NA, 1, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ hhclean1       <dbl> NA, 3, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ tiredhm1       <dbl> NA, 0, NA, 2, NA, NA, NA, NA, 2, NA, NA, NA, …
$ jobvsfa1       <dbl> NA, 0, NA, 2, NA, NA, NA, NA, 4, NA, NA, NA, …
$ tiredwk1       <dbl> NA, 0, NA, 3, NA, NA, NA, NA, 4, NA, NA, NA, …
$ famvswk1       <dbl> NA, 0, NA, 3, NA, NA, NA, NA, 2, NA, NA, NA, …
$ rfamlook       <dbl> NA, 2, NA, 0, NA, NA, NA, NA, 97, NA, NA, NA,…
$ spfalook       <dbl> NA, 2, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ stress         <dbl> 2, NA, 4, 3, NA, 2, 2, 3, 4, NA, NA, 4, 3, 3,…
$ supervis       <dbl> 2, NA, 1, 2, NA, 2, 2, 2, 1, NA, NA, 2, 1, 2,…
$ localnum       <dbl> 2, NA, 2, 2, NA, 2, 5, 6, 1, NA, NA, 1, 2, 4,…
$ hapunhap       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ madenkid       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relactiv       <dbl> 3, 2, 1, 1, 5, 1, 1, 2, 1, 8, 1, 1, 3, 1, 3, …
$ immcrime       <dbl> 5, 3, 2, 5, 2, 5, 3, 5, 3, NA, NA, 3, NA, 3, …
$ immjobs        <dbl> 5, 2, 1, 5, 2, 5, 4, 5, 3, NA, NA, 4, NA, 3, …
$ letin1a        <dbl> 2, 3, 5, 2, 5, 2, 3, 1, NA, NA, 3, NA, 3, 2, …
$ partners       <dbl> 0, NA, 0, NA, 1, 1, 4, 1, NA, 0, 0, 1, NA, 4,…
$ matesex        <dbl> NA, NA, NA, NA, 1, 1, 1, 1, NA, NA, NA, 2, NA…
$ frndsex        <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 1,…
$ acqntsex       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 2,…
$ pikupsex       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 2,…
$ paidsex        <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA, 2,…
$ othersex       <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA, NA…
$ sexsex         <dbl> NA, NA, NA, NA, 3, 3, 1, 3, NA, NA, NA, 1, NA…
$ sexfreq        <dbl> 0, NA, 0, NA, 2, 2, 6, 2, NA, 0, 0, NA, NA, 4…
$ numwomen       <dbl> 0, NA, 0, NA, 4, 15, 0, 5, NA, 0, NA, 0, NA, …
$ nummen         <dbl> 25, NA, 6, NA, 0, 0, 34, 0, NA, 3, NA, 1, NA,…
$ partnrs5       <dbl> 0, NA, 1, NA, 1, 1, 7, 1, NA, 0, 0, 1, NA, 4,…
$ sexsex5        <dbl> NA, NA, 1, NA, 3, 3, 1, 3, NA, NA, NA, 1, NA,…
$ evpaidsx       <dbl> 2, NA, 2, NA, 2, 2, 2, 2, NA, 2, 2, 2, NA, 2,…
$ evstray        <dbl> 2, NA, 1, 3, 3, 3, 3, 2, 3, 3, 2, 3, NA, 3, 3…
$ condom         <dbl> 2, NA, 2, NA, 2, 1, 1, 1, NA, 2, NA, 1, NA, 1…
$ relatsex       <dbl> 2, NA, 1, NA, 1, 1, 2, 1, NA, 1, NA, 1, NA, 1…
$ evidu          <dbl> 2, NA, 2, NA, 2, 2, 2, 2, NA, 2, 2, 2, NA, 2,…
$ idu30          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ evcrack        <dbl> 2, NA, 2, NA, 2, 2, 2, 2, NA, 2, 2, 2, NA, 2,…
$ crack30        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ hivtest        <dbl> 2, NA, 2, NA, 2, 2, 1, 2, NA, 2, 2, 1, NA, 2,…
$ hivtest1       <dbl> NA, NA, NA, NA, NA, NA, 201708, NA, NA, NA, N…
$ hivtest2       <dbl> NA, NA, NA, NA, NA, NA, 5, NA, NA, NA, NA, 1,…
$ sexornt        <dbl> 3, NA, 3, NA, 3, 3, 3, 3, NA, 3, 3, 3, NA, 3,…
$ realinc        <dbl> 40900.00, NA, 18405.00, 40900.00, 11247.50, 2…
$ realrinc       <dbl> 40900.00, NA, 18405.00, 2249.50, NA, 22495.00…
$ coninc         <dbl> 63300.00, NA, 28485.00, 63300.00, 17407.50, 3…
$ conrinc        <dbl> 63300.00, NA, 28485.00, 3481.50, NA, 34815.00…
$ ethnic         <dbl> 21, 2, 8, 15, 14, 8, 17, 17, 14, 30, 11, 15, …
$ eth1           <dbl> NA, 10, 14, 26, NA, 15, NA, 14, NA, NA, NA, 2…
$ eth2           <dbl> NA, NA, 11, 11, NA, NA, NA, NA, NA, NA, NA, N…
$ eth3           <dbl> NA, NA, NA, 14, NA, NA, NA, NA, NA, NA, NA, N…
$ hispanic       <dbl> 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 30, 1, 1, 1,…
$ racecen1       <dbl> 1, 1, 1, 1, 1, 1, 16, 1, 1, NA, 1, 1, 1, 1, 1…
$ racecen2       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ racecen3       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ uscitzn        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fucitzn        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ yearsusa       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mnthsusa       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ vetyears       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ dwelling       <dbl> 2, NA, NA, NA, NA, NA, 3, NA, 4, 6, NA, 8, 10…
$ dwelown        <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 2, 2, 2, NA, 3,…
$ dwelown16      <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 3, 1, NA, 2,…
$ worda          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 0, 1, NA, …
$ wordb          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 1, 1, NA, 1,…
$ wordc          <dbl> NA, 1, NA, 0, NA, NA, NA, NA, 1, 0, 1, NA, 0,…
$ wordd          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 1, 1, NA, 1,…
$ worde          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 1, 1, NA, 1,…
$ wordf          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 1, 0, 1, NA, 1,…
$ wordg          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 0, 0, 0, NA, …
$ wordh          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 0, 0, 1, NA, 1,…
$ wordi          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 1, 1, NA, …
$ wordj          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, 0, 0, 0, NA, 0,…
$ wordsum        <dbl> NA, 10, NA, 7, NA, NA, NA, NA, 7, 4, 8, NA, 8…
$ relate1        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ gender1        <dbl> 2, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 2…
$ old1           <dbl> 72, 80, NA, 57, NA, 27, NA, NA, NA, NA, NA, N…
$ mar1           <dbl> 3, 1, NA, 1, NA, 5, NA, NA, NA, NA, NA, NA, 1…
$ away1          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where1         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate2        <dbl> NA, 2, NA, 2, NA, 8, NA, NA, NA, NA, NA, NA, …
$ gender2        <dbl> NA, 2, NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, …
$ old2           <dbl> NA, 76, NA, 56, NA, 26, NA, NA, NA, NA, NA, N…
$ mar2           <dbl> NA, 1, NA, 1, NA, 5, NA, NA, NA, NA, NA, NA, …
$ away2          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where2         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate3        <dbl> NA, NA, NA, 3, NA, NA, NA, NA, NA, NA, NA, NA…
$ gender3        <dbl> NA, NA, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA…
$ old3           <dbl> NA, NA, NA, 23, NA, NA, NA, NA, NA, NA, NA, N…
$ mar3           <dbl> NA, NA, NA, 5, NA, NA, NA, NA, NA, NA, NA, NA…
$ away3          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where3         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate4        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender4        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old4           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar4           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away4          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where4         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate5        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender5        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old5           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar5           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away5          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where5         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate6        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender6        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old6           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar6           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away6          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where6         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate7        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender7        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old7           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar7           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away7          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where7         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate8        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender8        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old8           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar8           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away8          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where8         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate9        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender9        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old9           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar9           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away9          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where9         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate10       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender10       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old10          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar10          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away10         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where10        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate11       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender11       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old11          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar11          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away11         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where11        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate12       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender12       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old12          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar12          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away12         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where12        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate13       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ gender13       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ old13          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ mar13          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away13         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where13        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relate14       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ away14         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ where14        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd1        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ relhhd2        <dbl> NA, 2, NA, 2, NA, 3, NA, NA, NA, NA, NA, NA, …
$ relhhd3        <dbl> NA, NA, NA, 4, NA, NA, NA, NA, NA, NA, NA, NA…
$ relhhd4        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd5        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd6        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd7        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd8        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd9        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd10       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd11       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd12       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd13       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhhd14       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ hhrace         <dbl> NA, NA, NA, NA, NA, NA, 5, NA, 1, 2, NA, 1, 1…
$ respnum        <dbl> 1, 1, NA, 3, NA, 1, NA, NA, NA, NA, NA, NA, 4…
$ hhtype         <dbl> 1, 3, NA, 41, NA, 7, NA, NA, NA, NA, NA, NA, …
$ hhtype1        <dbl> 4, 1, NA, 1, NA, 5, NA, NA, NA, NA, NA, NA, 1…
$ famgen         <dbl> 1, 1, NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, 2…
$ rplace         <dbl> 1, 1, NA, 3, NA, 1, NA, NA, NA, NA, NA, NA, 4…
$ rvisitor       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ visitors       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ relhh1         <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, 1…
$ relhh2         <dbl> NA, 2, NA, 2, NA, 3, NA, NA, NA, NA, NA, NA, …
$ relhh3         <dbl> NA, NA, NA, 41, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh4         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh5         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh6         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh7         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh8         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh9         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh10        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh11        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh12        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh13        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relhh14        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp1         <dbl> NA, 2, NA, 2, NA, 3, NA, NA, NA, NA, NA, NA, …
$ relsp2         <dbl> NA, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, …
$ relsp3         <dbl> NA, NA, NA, 41, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp4         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp5         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp6         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp7         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp8         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp9         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp10        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp11        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp12        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp13        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ relsp14        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ dateintv       <dbl> 1019, 1116, 603, 718, 516, 1017, 728, 818, 80…
$ sei10          <dbl> 67.7, 73.9, 20.1, 17.0, 42.8, 20.1, 74.8, 84.…
$ sei10educ      <dbl> 76.9, 86.3, 38.4, 31.1, 37.4, 38.4, 85.7, 99.…
$ sei10inc       <dbl> 76.8, 79.7, 6.9, 5.5, 54.9, 6.9, 82.3, 72.2, …
$ pasei10        <dbl> 76.3, 26.8, 20.7, 26.8, 25.2, 62.0, 23.3, 32.…
$ pasei10educ    <dbl> 93.7, 24.3, 22.3, 24.3, 20.4, 73.0, 24.1, 25.…
$ pasei10inc     <dbl> 72.3, 26.7, 14.7, 26.7, 26.6, 68.1, 18.9, 39.…
$ masei10        <dbl> 62.9, NA, 21.6, 84.2, 38.8, 37.6, NA, 41.8, 1…
$ masei10educ    <dbl> 90.6, NA, 35.0, 97.8, 57.6, 58.9, NA, 59.2, 4…
$ masei10inc     <dbl> 43.6, NA, 9.9, 80.3, 27.8, 24.3, NA, 33.0, 5.…
$ spsei10        <dbl> NA, 59.1, NA, NA, NA, NA, NA, 84.5, NA, NA, N…
$ spsei10educ    <dbl> NA, 83.0, NA, NA, NA, NA, NA, 99.1, NA, NA, N…
$ spsei10inc     <dbl> NA, 48.2, NA, NA, NA, NA, NA, 72.2, NA, NA, N…
$ cosei10        <dbl> NA, NA, NA, NA, 24.2, 43.0, NA, NA, NA, NA, N…
$ cosei10educ    <dbl> NA, NA, NA, NA, 40.8, 55.4, NA, NA, NA, NA, N…
$ cosei10inc     <dbl> NA, NA, NA, NA, 11.3, 39.1, NA, NA, NA, NA, N…
$ copres10       <dbl> NA, NA, NA, NA, 48, 38, NA, NA, NA, NA, NA, N…
$ copres105plus  <dbl> NA, NA, NA, NA, 50, 39, NA, NA, NA, NA, NA, N…
$ uswary         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, NA, NA, NA…
$ cohort         <dbl> 1950, 1942, 1965, 1999, 1960, 1995, 2002, 197…
$ marcohrt       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ zodiac         <dbl> 1, 10, 4, 3, 11, 9, 12, 11, 11, 9, 12, 5, 4, …
$ inthisp        <dbl> 0, NA, NA, NA, NA, NA, 0, NA, 0, 0, NA, 0, 0,…
$ intrace1       <dbl> 1, NA, NA, NA, NA, NA, 1, NA, 1, 1, NA, 1, 1,…
$ intrace2       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ intrace3       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ whoelse1       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 1, 2, NA, 2, 2,…
$ whoelse2       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 2, 2, NA, 2, 2,…
$ whoelse3       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 2, 2, NA, 2, 1,…
$ whoelse4       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 2, 2, NA, 2, 2,…
$ whoelse5       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 2, 2, NA, 2, 2,…
$ whoelse6       <dbl> 2, NA, NA, NA, NA, NA, 2, NA, 2, 2, NA, 2, 2,…
$ intid          <dbl> 1, NA, NA, NA, NA, NA, 59, NA, 59, 59, NA, 59…
$ feeused        <dbl> 1, NA, NA, NA, NA, NA, 1, NA, NA, 3, NA, NA, …
$ feelevel       <dbl> 75, NA, NA, NA, NA, NA, 75, NA, NA, NA, NA, N…
$ lngthinv       <dbl> 105, 83, 156, 89, 80, 56, 88, 95, 123, 119, 3…
$ intethn        <dbl> 1, NA, NA, NA, NA, NA, 1, NA, 1, 1, NA, 1, 1,…
$ mode           <dbl> 3, 4, 4, 4, 4, 4, 1, 4, 1, 1, 4, 1, 1, 4, 3, …
$ consent        <dbl> NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, 1, NA,…
$ adminconsent   <dbl> 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, …
$ letdie1y       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 1, 1, 1, NA, …
$ ballot         <dbl> 3, 1, 3, 1, 3, 3, 3, 3, 1, 2, 2, 3, 2, 3, 1, …
$ version        <dbl> 3, 1, 3, 1, 3, 3, 3, 3, 1, 2, 2, 3, 2, 3, 1, …
$ issp           <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, …
$ formwt         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ sampcode       <dbl> 601, 601, 601, 601, 601, 601, 601, 601, 601, …
$ sample         <dbl> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1…
$ oversamp       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ phase          <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ spanself       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spanint        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ spaneng        <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ hlthstrt       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, 1, 2, NA, 1, N…
$ huadd          <dbl> NA, NA, NA, NA, NA, 1, NA, NA, NA, 1, NA, 1, …
$ huaddwhy       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ dwellpre       <dbl> NA, NA, NA, NA, NA, 4, NA, NA, NA, 6, NA, 7, …
$ kidsinhh       <dbl> NA, NA, NA, NA, NA, 2, NA, NA, NA, 2, NA, 2, …
$ respond        <dbl> NA, NA, NA, NA, NA, 1, NA, NA, NA, 1, NA, 1, …
$ incuspop       <dbl> NA, NA, NA, NA, NA, 2, NA, NA, NA, 3, NA, 3, …
$ neisafe        <dbl> NA, NA, NA, NA, NA, 2, NA, NA, NA, 2, NA, 2, …
$ rlooks         <dbl> 3, NA, NA, NA, NA, NA, 5, NA, 5, 5, NA, 4, 4,…
$ rgroomed       <dbl> 3, NA, NA, NA, NA, NA, 3, NA, 3, 4, NA, 3, 3,…
$ rhlthend       <dbl> 2, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ vstrat         <dbl> 2661, 2661, 2661, 2661, 2661, 2661, 2661, 266…
$ vpsu           <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, …
$ kish           <dbl> 123126, 112214, 121324, 121324, 111231, 12114…
$ famdif16y      <dbl> NA, NA, 2, NA, NA, NA, NA, NA, 2, 1, NA, NA, …
$ pawrkslf2      <dbl> 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, NA, 3, 1, 1, NA…
$ mawrkslf2      <dbl> 1, NA, 1, 1, 1, 1, NA, 1, 2, NA, 1, 3, 1, 1, …
$ ethworld1      <dbl> 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, …
$ ethworld2      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, …
$ ethworld3      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethworld4      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethworld5      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethworld6      <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethworld7      <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, …
$ ethworld8      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethworld9      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion1     <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion2     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion3     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion4     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion5     <dbl> 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion6     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion7     <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, …
$ ethregion8     <dbl> 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, …
$ ethregion9     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion10    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion11    <dbl> 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, …
$ ethregion12    <dbl> 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, …
$ ethregion13    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion14    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion15    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion16    <dbl> 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, …
$ ethregion17    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion18    <dbl> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion19    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion20    <dbl> 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion21    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, …
$ ethregion22    <dbl> 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion23    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion24    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion25    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion26    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion27    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion28    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion29    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion30    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion31    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion32    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion33    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion34    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion35    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion36    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion37    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion38    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion39    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion40    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion41    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion42    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion43    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion44    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion45    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion46    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion47    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion48    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion49    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion50    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion51    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion52    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion53    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion54    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion55    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion56    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion57    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion58    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion59    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion60    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion61    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion62    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion63    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion64    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion65    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion66    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion67    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion68    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion69    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion70    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion71    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion72    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion73    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion74    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion75    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion76    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion77    <dbl> 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion78    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion79    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion80    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion81    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, …
$ ethregion82    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion83    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion84    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion85    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion86    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion87    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion88    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion89    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion90    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion91    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion92    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion93    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion94    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ethregion96    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ wrkgovt1       <dbl> 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, …
$ wrkgovt2       <dbl> 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, …
$ spkathy        <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 1, NA, NA, 1, NA,…
$ libathy        <dbl> NA, NA, 2, NA, 2, NA, 2, 2, 2, NA, NA, 2, NA,…
$ spkracy        <dbl> NA, NA, 1, NA, 1, NA, 2, 2, 1, NA, NA, 2, NA,…
$ libracy        <dbl> NA, NA, 2, NA, 2, NA, 1, 1, 2, NA, NA, 1, NA,…
$ spkcomy        <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 2, NA, NA, 1, NA,…
$ colcomy        <dbl> NA, NA, 1, NA, 1, NA, 2, 2, 1, NA, NA, 2, NA,…
$ libcomy        <dbl> NA, NA, 2, NA, 2, NA, 1, 2, 2, NA, NA, 2, NA,…
$ spkmslmy       <dbl> NA, NA, 1, NA, 1, NA, 1, 1, 2, NA, NA, NA, NA…
$ libmslmy       <dbl> NA, NA, 2, NA, 2, NA, 2, 2, 1, NA, NA, 2, NA,…
$ polhitoky      <dbl> NA, NA, 1, NA, 2, NA, 1, 1, NA, 1, 1, 1, NA, …
$ polabusey      <dbl> NA, NA, 2, NA, 2, NA, 2, 2, NA, 2, 2, 1, NA, …
$ polattaky      <dbl> NA, NA, 1, NA, 1, NA, 1, 1, NA, 1, 1, 1, NA, …
$ raceacs1       <dbl> 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, …
$ raceacs2       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, …
$ raceacs3       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, …
$ raceacs4       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs5       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs6       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs7       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs8       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs9       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs10      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs11      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs12      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs13      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs14      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs15      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ raceacs16      <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, …
$ abdefectg      <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ abnomoreg      <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ abhlthg        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ abpoorg        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ abrapeg        <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ absingleg      <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ suicide1g      <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ suicide2g      <dbl> NA, 1, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ suicide3g      <dbl> NA, 1, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ suicide4g      <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ maborn         <dbl> 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, …
$ paborn         <dbl> 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, NA,…
$ sexbirth1      <dbl> 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, …
$ sexnow1        <dbl> 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, …
$ hivafraid      <dbl> 1, NA, 1, NA, 2, 1, 2, 2, NA, 2, 1, 2, NA, 3,…
$ hivimmrl       <dbl> 1, NA, 1, NA, 3, 1, 1, 1, NA, 2, 1, 1, NA, 3,…
$ hivdscrm       <dbl> 4, NA, 2, NA, 2, 4, 1, 3, NA, 3, 4, 3, NA, 3,…
$ ptnrornt       <dbl> 3, NA, 3, NA, 3, 3, 3, 3, NA, 3, NA, 3, NA, 3…
$ ptnrsxbrth     <dbl> 1, NA, 1, NA, 2, 2, 1, 2, NA, 1, NA, 1, NA, 1…
$ ptnrsxnow      <dbl> 1, NA, 1, NA, 2, 2, 1, 2, NA, 1, NA, 1, NA, 1…
$ conpharvacy    <dbl> 1, NA, NA, 1, 3, NA, NA, NA, NA, NA, 2, NA, N…
$ confedvacy     <dbl> 1, NA, NA, 2, 3, NA, NA, NA, NA, NA, 1, NA, N…
$ wtssps         <dbl> 0.2310947, 0.5769942, 1.0141485, 0.9018125, 1…
$ wtssnrps       <dbl> 0.3009903, 0.7419649, 1.3638342, 1.2022913, 1…
$ uswaryv        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ prayerv        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA…
$ courtsv        <dbl> NA, NA, 3, NA, 3, NA, NA, 1, NA, NA, 3, NA, N…
$ discaffwv      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA…
$ racopenv       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ getaheadv      <dbl> NA, NA, 1, NA, 1, NA, NA, 3, NA, NA, NA, NA, …
$ divlawv        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3, NA…
$ helpfulv       <dbl> NA, NA, 1, NA, 2, NA, NA, 3, NA, NA, 3, NA, N…
$ fairv          <dbl> NA, NA, 3, NA, 1, NA, NA, 3, NA, NA, 2, NA, N…
$ trustv         <dbl> NA, NA, 2, NA, 2, NA, NA, 3, NA, NA, 2, NA, N…
$ agedv          <dbl> NA, NA, 1, NA, 2, NA, NA, 3, NA, NA, 1, NA, N…
$ grassv         <dbl> NA, NA, 1, NA, NA, NA, NA, 1, NA, NA, 1, NA, …
$ relitenv       <dbl> NA, NA, 2, NA, 2, NA, NA, 4, NA, NA, 4, NA, N…
$ biblev         <dbl> NA, NA, 2, NA, 2, NA, NA, 3, NA, NA, 3, NA, N…
$ postlifev      <dbl> NA, NA, 1, NA, 1, NA, NA, 2, NA, NA, 1, NA, N…
$ kidssolv       <dbl> NA, NA, 4, NA, 3, NA, NA, 6, NA, NA, 5, NA, N…
$ uscitznv       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fucitznv       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fepolv         <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2, NA…
$ uswarynv       <dbl> NA, 1, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ prayernv       <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ courtsnv       <dbl> 1, 2, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ discaffwnv     <dbl> NA, 2, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ racopennv      <dbl> 2, 2, NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, N…
$ getaheadnv     <dbl> 1, 1, NA, 3, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ divlawnv       <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ helpfulnv      <dbl> 1, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ fairnv         <dbl> 1, NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, NA,…
$ trustnv        <dbl> 2, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ agednv         <dbl> 2, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ grassnv        <dbl> 1, NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, NA,…
$ relitennv      <dbl> 4, 2, NA, 4, NA, 4, NA, NA, NA, NA, NA, NA, N…
$ biblenv        <dbl> 3, 3, NA, 3, NA, 3, NA, NA, NA, NA, NA, NA, N…
$ postlifenv     <dbl> 2, 2, NA, 1, NA, 2, NA, NA, NA, NA, NA, NA, N…
$ kidssolnv      <dbl> 4, NA, NA, NA, NA, 5, NA, NA, NA, NA, NA, NA,…
$ uscitznnv      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fucitznnv      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ fepolnv        <dbl> NA, 2, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ abanyg         <dbl> 1, 1, NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, N…
$ fileversion    <dbl> 7222.4, 7222.4, 7222.4, 7222.4, 7222.4, 7222.…
$ childsinhh     <dbl> 0, 0, NA, 0, NA, 0, NA, NA, NA, NA, NA, NA, 2…
$ adultsinhh     <dbl> 1, 2, NA, 3, NA, 2, NA, NA, NA, NA, NA, NA, 4…
$ racerank1      <dbl> 1, 1, 1, 1, 1, 1, 16, 1, 1, NA, 1, 1, 1, 1, 1…
$ racerank2      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ racerank3      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ racopeny       <dbl> NA, NA, 1, NA, 2, NA, 2, 2, 2, NA, NA, 2, NA,…
$ adoptus        <dbl> 3, 1, 3, 3, 1, 3, 3, 3, 3, NA, NA, 3, NA, 3, …
$ immfate        <dbl> 1, 1, 3, 1, 3, 1, 2, 1, NA, NA, NA, 1, NA, 1,…
$ vote20         <dbl> 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, …
$ pres20         <dbl> 1, 1, 2, 1, 2, 1, NA, 1, 1, 1, 1, 1, 3, 2, 2,…
$ if20who        <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA, NA…
$ wordk          <dbl> NA, 1, NA, 0, NA, NA, NA, NA, NA, NA, NA, NA,…
$ wordl          <dbl> NA, 1, NA, 0, NA, NA, NA, NA, NA, NA, NA, NA,…
$ wordn          <dbl> NA, 1, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ fechld2        <dbl> NA, 3, NA, 2, NA, NA, NA, NA, NA, NA, NA, NA,…
$ fepresch2      <dbl> NA, 2, NA, 4, NA, NA, NA, NA, NA, NA, NA, NA,…
$ rspgndr        <dbl> NA, 3, NA, 5, NA, NA, NA, NA, 3, NA, NA, NA, …
$ prntlk         <dbl> NA, 2, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ prntfnce       <dbl> NA, 5, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ prntcre        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 3, NA, NA, NA…
$ prntply        <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ prntbhav       <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ prntadvs       <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ prntmdl        <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ orginc         <dbl> NA, 4, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ plan1          <dbl> NA, 4, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ sharehhw       <dbl> NA, 3, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ clsrltv        <dbl> NA, 2, NA, 2, NA, NA, NA, NA, 3, NA, NA, NA, …
$ rsprltv1       <dbl> NA, 6, NA, 5, NA, NA, NA, NA, 4, NA, NA, NA, …
$ rsprltv2       <dbl> NA, 6, NA, 4, NA, NA, NA, NA, 2, NA, NA, NA, …
$ eldfnce        <dbl> NA, 5, NA, 4, NA, NA, NA, NA, 4, NA, NA, NA, …
$ rlyrltv        <dbl> NA, 9, NA, 1, NA, NA, NA, NA, 6, NA, NA, NA, …
$ frndfam        <dbl> NA, 3, NA, 4, NA, NA, NA, NA, 4, NA, NA, NA, …
$ cabgndr        <dbl> NA, 3, NA, 2, NA, NA, NA, NA, 3, NA, NA, NA, …
$ univgndr       <dbl> NA, 3, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ execgndr       <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 3, NA, NA, NA, …
$ yrfnce         <dbl> NA, 4, NA, 3, NA, NA, NA, NA, 4, NA, NA, NA, …
$ nmbrkids       <dbl> NA, 2, NA, 1, NA, NA, NA, NA, 2, NA, NA, NA, …
$ conhlth        <dbl> 3, NA, 4, NA, 4, 5, 3, 3, NA, NA, NA, 3, NA, …
$ hlthbtr        <dbl> 5, NA, 3, NA, 5, 5, 4, 5, NA, NA, NA, 5, NA, …
$ hlthmore       <dbl> NA, NA, 4, NA, 2, 5, 3, 4, NA, NA, NA, 4, NA,…
$ hlthgov        <dbl> 5, NA, 2, NA, 5, 5, 4, 5, NA, NA, NA, 4, NA, …
$ hlthinf        <dbl> 2, NA, 4, NA, 2, 1, 3, 1, NA, NA, NA, 2, NA, …
$ hlthtax        <dbl> 2, NA, 4, NA, 5, 2, 2, 1, NA, NA, NA, 2, NA, …
$ hlthctzn       <dbl> 3, NA, 2, NA, 5, 1, 2, 1, NA, NA, NA, 2, NA, …
$ hlthdmg        <dbl> 2, NA, 2, NA, 5, 1, 2, 1, NA, NA, NA, 2, NA, …
$ hlthacc1       <dbl> 1, NA, 1, NA, 1, 1, 1, 1, NA, NA, NA, 1, NA, …
$ hlthacc2       <dbl> 5, NA, 3, NA, 4, 3, 5, 3, NA, NA, NA, 3, NA, …
$ hlthacc3       <dbl> 4, NA, 3, NA, 3, 4, 5, 4, NA, NA, NA, 4, NA, …
$ hlthacc4       <dbl> 1, NA, 3, NA, NA, 5, 2, 1, NA, NA, NA, NA, NA…
$ hlthbeh        <dbl> 3, NA, 3, NA, 3, 3, 2, 5, NA, NA, NA, 4, NA, …
$ hlthenv        <dbl> 3, NA, 3, NA, 3, 3, 2, 1, NA, NA, NA, 2, NA, …
$ hlthgene       <dbl> 3, NA, 2, NA, 3, 3, 2, 3, NA, NA, NA, 2, NA, …
$ hlthpoor       <dbl> 3, NA, 3, NA, 3, 1, 3, 1, NA, NA, NA, 2, NA, …
$ altmed         <dbl> 4, NA, 3, NA, 3, 3, 2, 3, NA, NA, NA, 3, NA, …
$ doctrst        <dbl> 2, NA, 2, NA, 4, 3, 3, 2, NA, NA, NA, 3, NA, …
$ docskls        <dbl> 3, NA, 4, NA, 2, 3, 4, 2, NA, NA, NA, 2, NA, …
$ docearn        <dbl> 3, NA, 3, NA, 2, 3, 3, 4, NA, NA, NA, 3, NA, …
$ hlthweb        <dbl> 4, NA, 5, NA, 4, 1, 5, 4, NA, NA, NA, 4, NA, …
$ hlthwblif      <dbl> 4, NA, 2, NA, 2, 5, 5, 3, NA, NA, NA, 3, NA, …
$ hlthwbanx      <dbl> 4, NA, 1, NA, 1, 5, 4, 3, NA, NA, NA, 3, NA, …
$ hlthwbvax      <dbl> 3, NA, 2, NA, 1, 5, 4, 2, NA, NA, NA, 3, NA, …
$ webhltbeh      <dbl> 3, NA, 4, NA, 3, 5, 3, 2, NA, NA, NA, 4, NA, …
$ webdocexp      <dbl> 3, NA, 4, NA, 3, 3, 2, 2, NA, NA, NA, 2, NA, …
$ websympt       <dbl> 2, NA, 4, NA, 3, 3, 4, 2, NA, NA, NA, 2, NA, …
$ webdradv       <dbl> 2, NA, 4, NA, 3, 3, 4, 2, NA, NA, NA, 2, NA, …
$ webrely        <dbl> 2, NA, 1, NA, 2, 3, 3, 4, NA, NA, NA, 4, NA, …
$ vaxdoharm      <dbl> 5, NA, 4, NA, 2, 3, 3, 5, NA, NA, NA, 4, NA, …
$ immunbetr      <dbl> 5, NA, 2, NA, 3, 3, 3, 5, NA, NA, NA, 4, NA, …
$ hlthprb        <dbl> 3, NA, 1, NA, 4, 3, 3, 2, NA, NA, NA, 2, NA, …
$ hlthpain       <dbl> 4, NA, 2, NA, 5, 3, 1, 3, NA, NA, NA, 3, NA, …
$ hlthdep        <dbl> 4, NA, 2, NA, 1, 3, 3, 2, NA, NA, NA, 2, NA, …
$ hlthconf       <dbl> 3, NA, 1, NA, 2, 3, 2, 2, NA, NA, NA, 3, NA, …
$ hlthnot        <dbl> 3, NA, 2, NA, 1, 3, 2, 2, NA, NA, NA, 1, NA, …
$ docvst         <dbl> 3, NA, 2, NA, 4, 3, 1, 2, NA, NA, NA, 2, NA, …
$ docalt         <dbl> 1, NA, 1, NA, 1, 3, 1, 1, NA, NA, NA, 1, NA, …
$ medpay         <dbl> 2, NA, 1, NA, 2, 1, 2, 2, NA, NA, NA, 1, NA, …
$ medcommt       <dbl> 1, NA, 2, NA, 2, 1, 2, 2, NA, NA, NA, 2, NA, …
$ medwtlst       <dbl> 2, NA, 2, NA, 2, 1, 2, 1, NA, NA, NA, 2, NA, …
$ medbest        <dbl> 2, NA, 3, NA, 3, 4, 3, 2, NA, NA, NA, 2, NA, …
$ hlthsat        <dbl> 3, NA, 3, NA, 5, 4, 3, 3, NA, NA, NA, 6, NA, …
$ docsat1        <dbl> 1, NA, 1, NA, 4, 4, 2, 3, NA, NA, NA, 3, NA, …
$ altsat         <dbl> 8, NA, 8, NA, 8, 4, 8, 8, NA, NA, NA, 4, NA, …
$ smokeday       <dbl> 2, NA, 5, NA, 5, 1, 1, 1, NA, NA, NA, 1, NA, …
$ drinkday1      <dbl> 1, NA, 1, NA, 3, 1, 1, 1, NA, NA, NA, 2, NA, …
$ physact        <dbl> 2, NA, 2, NA, 3, 4, 4, 2, NA, NA, NA, 3, NA, …
$ frtvegs        <dbl> 5, NA, 3, NA, 4, 4, 5, 5, NA, NA, NA, 5, NA, …
$ disblty        <dbl> 2, NA, 2, NA, 1, 2, 2, 2, NA, NA, NA, 1, NA, …
$ weight_issp    <dbl> 172, NA, 128, NA, 175, 200, 175, 152, NA, NA,…
$ shutbus        <dbl> 1, NA, 3, NA, 1, 1, 2, 1, NA, NA, NA, 1, NA, …
$ stayhome       <dbl> 1, NA, 3, NA, 2, 1, 1, 2, NA, NA, NA, 2, NA, …
$ mobilsurv      <dbl> 1, NA, 4, NA, 3, 1, 2, 4, NA, NA, NA, 3, NA, …
$ reqmasks       <dbl> 1, NA, 3, NA, 1, 1, 1, 1, NA, NA, NA, 1, NA, …
$ bangather      <dbl> 1, NA, 3, NA, 1, 1, 1, 2, NA, NA, NA, 1, NA, …
$ stockval1      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ stockyr        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ stockyrval     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ stockoptyr     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ stoptyramt     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ extr2021       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, NA, NA, 2,…
$ extraval1      <dbl> NA, NA, NA, NA, NA, NA, 2, NA, NA, NA, NA, NA…
$ yearval1       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 4…
$ numorg1        <dbl> 4, NA, NA, NA, NA, 2, 4, 5, NA, NA, NA, 1, 11…
$ perfrt         <dbl> 3, NA, 4, NA, NA, 3, 3, 4, NA, NA, NA, 3, 3, …
$ chngtime       <dbl> 1, NA, 3, 1, NA, 4, 3, 1, 2, NA, NA, 1, 2, 4,…
$ wrkmeangfl     <dbl> 3, NA, 2, 4, NA, 1, 2, 2, 1, NA, NA, 2, 2, 2,…
$ strmgtsup      <dbl> 4, NA, 2, 2, NA, 1, 3, 3, 5, NA, NA, 4, 4, 3,…
$ psysamephys    <dbl> 4, NA, 2, 1, NA, 1, 2, 3, 3, NA, NA, 4, 3, 3,…
$ allorglevel    <dbl> 2, NA, 2, 1, NA, 5, 2, 3, 4, NA, NA, 4, 3, 3,…
$ feelnerv       <dbl> 2, NA, 1, 2, NA, 3, 3, 2, 1, NA, NA, 2, 3, 1,…
$ worry          <dbl> 2, NA, 1, 1, NA, 2, 2, 1, 1, NA, NA, 2, 2, 1,…
$ feeldown       <dbl> 2, NA, 1, 1, NA, 2, 3, 1, 1, NA, NA, 1, 1, 1,…
$ nointerest     <dbl> 2, NA, 1, 1, NA, 3, 2, 1, 1, NA, NA, 1, 1, 1,…
$ svyenjoy       <dbl> 2, 4, 2, 4, 5, 2, 2, 5, 2, 3, 2, 4, 2, 3, 1, …
$ svyid1         <dbl> 2, 3, 2, 4, 4, 3, 2, 4, 1, 2, 3, 3, 2, 1, 2, …
$ svyid2         <dbl> 1, 3, 3, 4, 4, 3, 2, 4, 2, 1, 4, 3, 2, 3, 1, …
$ baselinestatus <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ amerstatus     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ yrlvmus        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 1, NA,…
$ yrartxbt       <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ yrmovie        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 1, NA,…
$ artsout        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA…
$ yrcreat        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, NA, NA…
$ yrrdg          <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 1, NA,…
$ yrtour         <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ yrstmus        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 1, NA,…
$ yrarmus        <dbl> NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, 1, NA,…
$ yrstpo         <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ yrarpo         <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ yrclass        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ yrpod          <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 1, NA,…
$ cvdlvmus       <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 1, NA,…
$ cvdart         <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 3, NA,…
$ cvdmov         <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 1, NA,…
$ cvdcreat       <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 4, NA,…
$ cvdrdg         <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 1, NA,…
$ cvdtour        <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 2, NA,…
$ cvdstmus       <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 2, NA,…
$ cvdarmus       <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ cvdstpo        <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 4, NA,…
$ cvdarpo        <dbl> NA, NA, NA, NA, 2, NA, NA, NA, NA, NA, 2, NA,…
$ cvdclass       <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 4, NA,…
$ cvdpod         <dbl> NA, NA, NA, NA, 4, NA, NA, NA, NA, NA, 2, NA,…
$ neastatus      <dbl> NA, NA, NA, NA, 1, NA, NA, NA, NA, NA, 1, NA,…
$ wrkwayup_next  <dbl> 5, NA, NA, 5, 2, NA, NA, NA, NA, NA, 5, NA, N…
$ blkmblty       <dbl> 2, NA, NA, 1, 4, NA, NA, NA, NA, NA, 2, NA, N…
$ blkdsrv        <dbl> 1, NA, NA, 1, 3, NA, NA, NA, NA, NA, 3, NA, N…
$ blktry         <dbl> 5, NA, NA, 4, 2, NA, NA, NA, NA, NA, 5, NA, N…
$ brv5           <dbl> 1, NA, NA, 1, 0, NA, NA, NA, NA, NA, 1, NA, N…
$ brv5sp         <dbl> 0, NA, NA, 0, NA, NA, NA, NA, NA, NA, 1, NA, …
$ brv5par        <dbl> 0, NA, NA, 0, NA, NA, NA, NA, NA, NA, 0, NA, …
$ brv5grand      <dbl> 0, NA, NA, 0, NA, NA, NA, NA, NA, NA, 0, NA, …
$ brv5child      <dbl> 0, NA, NA, 0, NA, NA, NA, NA, NA, NA, 0, NA, …
$ brv5sib        <dbl> 0, NA, NA, 0, NA, NA, NA, NA, NA, NA, 1, NA, …
$ brv5oth        <dbl> 1, NA, NA, 1, NA, NA, NA, NA, NA, NA, 0, NA, …
$ brv5spnum      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA…
$ brv5partnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0, NA…
$ brv5dadnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5momnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5filnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5milnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5gmanum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5gpanum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5sonnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5daunum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5chinum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5bronum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2, NA…
$ brv5sisnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0, NA…
$ brv5silnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0, NA…
$ brv5cuznum     <dbl> 1, NA, NA, 1, NA, NA, NA, NA, NA, NA, NA, NA,…
$ brv5frndnum    <dbl> 2, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ brv5cowknum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv5othnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16          <dbl> 1, NA, NA, 1, 1, NA, NA, NA, NA, NA, 1, NA, N…
$ brv16sp        <dbl> 0, NA, NA, 0, 0, NA, NA, NA, NA, NA, 0, NA, N…
$ brv16par       <dbl> 0, NA, NA, 0, 0, NA, NA, NA, NA, NA, 0, NA, N…
$ brv16sib       <dbl> 0, NA, NA, 0, 0, NA, NA, NA, NA, NA, 0, NA, N…
$ brv16grand     <dbl> 1, NA, NA, 1, 1, NA, NA, NA, NA, NA, 0, NA, N…
$ brv16oth       <dbl> 0, NA, NA, 0, 0, NA, NA, NA, NA, NA, 1, NA, N…
$ brv16spnum     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16partnum   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16dadnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16momnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16filnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16milnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16gmanum    <dbl> 1, NA, NA, NA, 0, NA, NA, NA, NA, NA, NA, NA,…
$ brv16gpanum    <dbl> 1, NA, NA, 2, 0, NA, NA, NA, NA, NA, NA, NA, …
$ brv16bronum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16sisnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16silnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ brv16cuznum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1, NA…
$ brv16frndnum   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0, NA…
$ brv16othnum    <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0, NA…
$ gestate        <dbl> NA, NA, NA, 1, 2, NA, NA, NA, NA, NA, 1, NA, …
$ abgender       <dbl> 2, NA, NA, 2, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ abbelief       <dbl> 1, NA, NA, 1, 3, NA, NA, NA, NA, NA, 1, NA, N…
$ vaxhstncy      <dbl> 5, NA, NA, 4, 4, NA, NA, NA, NA, NA, 5, NA, N…
$ vaxkids        <dbl> 1, NA, NA, 2, 3, NA, NA, NA, NA, NA, 1, NA, N…
$ vaxsafe        <dbl> 1, NA, NA, 2, 4, NA, NA, NA, NA, NA, 2, NA, N…
$ fluvax         <dbl> 1, NA, NA, 2, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ covid12        <dbl> 1, NA, NA, 1, 2, NA, NA, NA, NA, NA, 1, NA, N…
$ covemply       <dbl> 2, NA, NA, NA, 1, NA, NA, NA, NA, NA, 5, NA, …
$ pandinc        <dbl> 3, NA, NA, 2, 3, NA, NA, NA, NA, NA, 2, NA, N…
$ pandmet        <dbl> 4, NA, NA, 2, 3, NA, NA, NA, NA, NA, 1, NA, N…
$ biokids        <dbl> 1, NA, NA, 0, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ malekids       <dbl> 0, NA, NA, 0, 1, NA, NA, NA, NA, NA, 0, NA, N…
$ firstkidsex    <dbl> 2, NA, NA, NA, 1, NA, NA, NA, NA, NA, 2, NA, …
$ nonbinkids     <dbl> 2, NA, NA, 2, 2, NA, NA, NA, NA, NA, 2, NA, N…
$ femself        <dbl> 5, NA, NA, 6, 1, NA, NA, NA, NA, NA, 5, NA, N…
$ mascself       <dbl> NA, NA, NA, 1, 7, NA, NA, NA, NA, NA, 1, NA, …
$ nextstatus     <dbl> 1, NA, NA, 1, 1, NA, NA, NA, NA, NA, 1, NA, N…
$ worksick       <dbl> 90, NA, 0, 3, NA, 0, 1, 0, 3, NA, NA, 5, 3, 0…
$ fund_next      <dbl> 3, NA, NA, 3, 2, NA, NA, NA, NA, NA, 3, NA, N…
$ hompop_exp     <dbl> 1, 1, 3, 1, 3, 1, 3, 2, 2, 1, 2, 1, 1, 1, 3, …
$ modesequence   <dbl> 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, …
$ rheight        <dbl> 64, NA, 63, NA, 71, 72, 63, 69, NA, NA, NA, 6…
$ instype01      <dbl> 3, NA, 5, NA, 1, 1, 1, 3, NA, NA, NA, 2, NA, …
$ instype02      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ instype03      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ instype04      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ totalincentive <dbl> 177, 200, 52, 127, 87, 102, 102, 57, 102, 2, …
$ babies_exp     <dbl> NA, NA, 0, NA, 0, NA, 0, 0, 1, 0, 0, 0, NA, N…
$ preteen_exp    <dbl> NA, NA, 0, NA, 0, NA, 0, 0, 0, 0, 0, 0, NA, N…
$ teens_exp      <dbl> NA, NA, 0, NA, 0, NA, 2, 0, 0, 0, 0, 0, NA, N…
$ adults_exp     <dbl> NA, NA, 3, NA, 3, NA, 1, 2, 1, 1, 2, 1, NA, N…
$ childs_exp     <dbl> NA, NA, 0, NA, 0, NA, 2, 0, 1, 0, 0, 0, NA, N…
$ respnumh       <dbl> 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 1, 2, …
$ hefinfo1       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ famgen_exp     <dbl> NA, NA, 2, NA, 2, NA, 1, 1, 2, 1, 2, 1, NA, N…
$ hhtype1_exp    <dbl> NA, NA, 3, NA, 5, NA, 2, 1, 2, 4, 3, 4, NA, N…
$ batch          <dbl> NA, 2, 1, 2, 1, NA, 2, NA, 2, NA, 2, NA, NA, …
$ subsamprate    <dbl> 1.0, NA, NA, NA, NA, 1.0, NA, 1.0, NA, 1.0, N…
$ wtssps_nea     <dbl> NA, NA, NA, NA, 1.7044439, NA, NA, NA, NA, NA…
$ wtssnrps_nea   <dbl> NA, NA, NA, NA, 3.2197778, NA, NA, NA, NA, NA…
$ wtssps_next    <dbl> 0.2309795, NA, NA, 0.8807435, 1.6932353, NA, …
$ wtssnrps_next  <dbl> 0.2674994, NA, NA, 1.0893818, 2.1217118, NA, …
$ wtssps_as      <dbl> 0.2764242, 0.6735305, 1.2107570, 1.0831560, 1…
$ wtssnrps_as    <dbl> 0.3762613, 0.8941144, 1.6817922, 1.4858712, 1…

Introducing abany

The GSS abany item asks “Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion if the woman wants it for any reason?” The answers are “yes” (1) and “no” (2).

There is also a web version of this in 2022: abanyng. We will drop this for now.

Warning

We do not want variables coded 1 and 2. As we will see later, it’s better if (almost) all variables have a meaningful 0 value.

Wrangling abany

d <- gss2022 |> 
  select(abany) 

d |> group_by(abany) |> 
  summarize(n = n())
# A tibble: 3 × 2
  abany     n
  <dbl> <int>
1     1   799
2     2   546
3    NA  2804
d <- d |> 
  drop_na() |>   # drop NA values
  mutate(abany = case_match(abany,
                            1 ~ 1,
                            2 ~ 0 ))

d |> pull(abany) |> table()

  0   1 
546 799

Tip

case_match() is useful for recoding variables.

abany sample proportion

We can use mean() to calculate the sample proportion.

mean(d$abany)
[1] 0.594052

We find that 59.4% of our sample supports abortion rights for any reason.

Inference

How close is this sample statistic to the population parameter? We’ll never know.

We can use a simulation to give us a sense of what kind of accuracy is possible with a sample of 1345 respondents.

Random number functions

We could build an imaginary US adult population where 59.4% of adults support abortion rights. But we can instead use random number functions to draw a sample from an infinite population instead.

set.seed(722)
rbinom(n = 1345, size = 1, prob = .594) |> # sample from inf. pop.
  mean()                                   # take the mean
[1] 0.5635688

Why 59.4%?

Why assume that the population parameter is .594? Because we are interested in how widely spread the simulations are and there isn’t a more reasonable value to choose.

Taking many samples (again)

Let’s do this 5000 times and collect the results.

set.seed(722)
gss_sims <- tibble(
  sim_id = 1:5000) |> 
  rowwise() |> 
  mutate(samp_prop = mean(rbinom(1345, 1, .594)))

The IQR tells us how spread out the middle half of the estimates are.

gss_sims |> pull(samp_prop) |> IQR()
[1] 0.01858736

Thus, with 1345 cases, half of the sample proportions will be within approximately 1.9 points of the true value.

Visualize

Summary

We still don’t know the true value, of course. We are probably within a couple of points of the true value. But we could be 3 (or possibly more) points away.

Recap

  • we want to know about populations
  • we end up having to use samples
  • samples are random subsets of the population that are expensive to collect
  • the larger the sample, the more accurately we can infer the population proportion
  • we can use simulations to understand how this works.

Homework

  • make a fake population of at least 100,000 inhabitants OR use random number functions
  • make some people do/think/believe/are X (1) and some people not-X (0)
  • write a function that samples from that population using 3 or more different sample sizes
  • plot and interpret your results
  • push it to GitHub the night before the next lecture

Message me on Slack if you are struggling!

Probability

From simulations to laws

We saw two things in the simulations:

  1. As the number of simulations gets bigger, the clearer the pattern we observe

  2. The pattern we see is a symmetrical distribution centered on the “true” value

This relates to two rules that are important in statistics.

Law of Large Numbers

The average of the results (e.g., means) obtained from a large number of independent random samples converges to the true value as the number of samples increases.

This applies to a single large sample or to the sum of many smaller samples (as we did with the simulations).

This only works because each observation (e.g., person) is randomly sampled.

Law of Large Numbers

The observed value eventually converges to .594. It’s still not perfect here!

Central limit theorem

In the long run, the distribution of averages of any distribution converges to the normal distribution.

Note

The normal distribution is that “bell-shaped” distribution you saw last time. We will define it more formally later on.

CLT demo

It doesn’t matter what the shape of the empirical distribution is. Repeated estimates of its mean will form a normal distribution.

tvdata <- gss2022 |> 
  select(tvhours) |> 
  drop_na()

ggplot(tvdata,
       aes(x = tvhours)) +
  geom_bar(fill = "gray")

CLT demo

Distribution of sampled means

# get sampling function
get_tv_mean <- function() {
  slice_sample(tvdata, 
               n = nrow(tvdata),  # sample size = data size
               replace = TRUE) |> # replacement
    pull(tvhours) |> 
    mean()
}

# draw samples
set.seed(722)
tv_samples <- tibble(
  samp_id = 1:5000) |> 
  rowwise() |> 
  mutate(samp_mean = get_tv_mean())

# plot
ggplot(tv_samples,
       aes(x = samp_mean)) +
  geom_histogram(fill = "gray",
                 color = "white",
                 binwidth = .025)

Distribution of sampled means

Summary

We will return to this. For now, it’s important to remember:

  1. The Law of Large Numbers states that repeated random observations will converge to the true value;

  2. The Central Limit Theorem states that estimates (e.g., means) from repeated random samples will form a normal distribution regardless of the data distribution.

Warning

Non-random samples, no matter how large, will not converge to the true population value!

Putting this into practice

We aren’t totally ready for this (and we’ll come back) but here’s why this matters. If we have a “large enough” sample (just one, real-life sample), we can use that to estimate the uncertainty of the sampling process.

For example, if we had a sample of 400, 70% of whom are parents, we could say that, if we repeated our experiment infinite times, 95% of the estimated sample proportions would be between .655 and .745.

The formula for this is \(\hat{p} \pm 1.96 \times \sqrt{\hat{p}(1-\hat{p}) / n}\). But don’t worry about that for now!

Probability basics

To really get this, we need probability. We haven’t defined it formally, but we’ve been using it in this course.

For example, when we defined a population of 100,000, exactly 70,000 of whom were parents, and sampled them at random, we made it so each “draw” had a probability of .7 of being a parent.

Note

Technically this isn’t true unless we do sampling with replacement. Otherwise the probability would change slightly with each draw.

Probability of an event

Let’s return to the abortion rights example. In the 2022 GSS, there are two possibilities: support abortion rights, \(S\), or oppose abortion rights, \(O\). These are complementary events, so \(O = \neg S\).

Together, these represent the event space, or the set of things that can happen in one event (sampling a person). We can write \(\Omega = \{S, \neg S\}\). These are mutually exclusive events.

Since 59.4% of sample respondents support, we can say \(P(S) = .594\) and \(P(\neg S) = .406\). \(P(x)\) or \(Pr(x)\) means “the probability of \(x\).”

Probability of two events

If \(P(S) = .594\), what is the probability of sampling two people in a row who both support abortion rights?

These events are independent so the probability is \(.594 \times .594 \approx .353\). Independent here means that the result of the each draw has no effect on the value of other draws.

Multiple attributes

Let’s look at a dataset with multiple variables per respondent. Let’s consider whether each respondent is “very happy” and whether the respondent has a college degree. To do this, we’ll need to do some wrangling.

d <- gss2022 |> 
  select(happy, educ) |> 
  drop_na() |> 
  mutate(vhappy = if_else(happy == 1, 
                          "Very happy", 
                          "Not very" ),
         college = if_else(educ >= 16, 
                           "College", 
                           "Not college")) |> 
  select(vhappy, college)

Contingency table

college Not very Very happy
College 1171 357
Not college 2055 510

This isn’t very “tidy” but we can wrangle this into a 2x2 table of counts of these variables. This is called a contingency table.

Marginal probability

college Not very Very happy
College 1171 357
Not college 2055 510

The marginal probability is the probability of an event related to one variable without regard for the the other variable.

So what is the marginal probability of having a college degree, \(P(\text{College})\)? What is the marginal probability of being very happy, \(P(\text{Very happy})\)?

Joint probability

college Not very Very happy
College 1171 357
Not college 2055 510

The joint probability is the probably of two events happening at the same time.

What is the joint probability of having a college degree and being very happy, \(P(\text{College} \cap \text{Very happy})\)?

Joint probability visualized

Product of marginal probabilities

Why isn’t the joint probability here (0.087) the same as the product of the marginal probabilities (0.079)?

What would it mean if this were true? (It’s not.)

\[P(\text{College}) \times P(\text{Very happy}) = \\ P(\text{College} \cap \text{Very happy})\]

It would mean that the two variables were independent, i.e., that knowing one tells you nothing about the other.

Conditional probability

The final type we’ll learn is conditional probability. This is the probability of a specific outcome conditional on the value of another variable.

Conditional example (1)

What is the probability of being very happy conditional on having a college degree?

college Not very Very happy
College 1171 357
Not college 2055 510

\(P(\text{VH} | \text{C}) =\) 0.234

Conditional example (2)

What is the probability of being very happy conditional on NOT having a college degree?

college Not very Very happy
College 1171 357
Not college 2055 510

\(P(\text{VH} | \neg \text{C}) =\) 0.199

If these conditional probabilities were the same, the two variables would be independent.

Conditional probability visualized

Summary

This is a very basic introduction to probability. We will build on it but it’s important to understand the fundamentals of marginal, joint, and conditional probability.

Homework

  1. Create two different two-by-two tables, at least one of which is from the GSS. Make sure to use drop_na() to exclude missing data for now.

  2. Compute and interpret all the marginal, joint, and conditional probabilities for each table.

Univariate statistics

Descriptive statistics

We will distinguish between descriptive statistics for three different variable types:

  1. Continuous (interval, ratio, and some ordinal variables)

  2. Binary

  3. Multinomial or categorical (nominal and some ordinal)

The right data

Let’s get a few variables to work with.

d <- gss2022 |>
  select(wordsum,      # continuous
         age,          # continuous
         educ,         # continuous (make binary/ordinal)
         marital) |>   # nominal
  drop_na() |> 
  mutate(marital_chr = case_match(marital,
                                  1 ~ "married",
                                  2 ~ "widowed",
                                  c(3,4) ~ "sep. or div.",
                                  5 ~ "never mar."))

Note

Deleting cases with any missing data is sometimes OK, but there are often better ways to handle it. We will address this (much) later!

Continuous: wordsum

How many of the following words can you correctly define (picking the closest synonym via multiple choice):

  • Adept
  • Audible
  • Consume
  • Coherent
  • Emulate
  • Erroneous
  • Fortitude
  • Misnomer
  • Reverent
  • Stimulus

I’m not 100% sure these are the words. But ChatGPT was pretty confident about it!

Continuous: wordsum

Center and spread

We can use numbers to summarize a variable from a sample rather than having to reproduce the entire column of data every time.

Center

  • mean
  • median
  • mode

Spread

  • variance
  • standard deviation
  • interquartile range

We will focus on the mean, variance, and standard deviation first.

Mean and notation

\(\bar{x}\) is pronounced “x-bar” and is the mean of the variable \(x\) in a particular sample. We often use \(x\) when we are talking about a variable.

\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \] \(\Sigma\) means to sum; \(i\) is an index for each observation; \(n\) is the number of observations in the sample. So we are summing the values of \(x\) for each observation from the first \((i=1)\) to the last \((i=n)\) and then dividing by \(n\).

Mean: wordsum

The mean is 6.36.

Variance

The sample variance tells you how spread out the data points are.

\[ s^2 = \frac{1}{n-1} \sum_{i=1}^{n}(x_i-\bar{x})^2 \] This is sort of the average squared deviation from the mean. We divide by \(n-1\) for reasons you don’t need to worry about right now. We use squared deviations instead of absolute deviations for many reasons we are also not going to talk about right now!

Standard deviation

The variance \((s^2)\) has many desirable properties we’re not ready to discuss. Its main disadvantage is that it’s in squared units of the variable. By taking the square root, we get an interpretable value.

\[ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i-\bar{x})^2} \] The standard deviation, \(s\), is a “typical deviation” from the mean.

Standard deviation: wordsum

The mean of wordsum is 6.36. The standard deviation is 2.22.

We’ll talk more about how to use these values soon. For now, just remember that a deviation from the mean of that size or less would not be unusual. So anything between

Sample and population

So far, we’ve defined and discussed these as sample statistics rather than population parameters. The notation is slightly different for populations (although researchers are not always consistent).

  • The sample mean is \(\bar{x}\); the population mean is \(\mu\).

  • The sample variance is \(s^2\); the population variance is \(\sigma^2\).

  • The sample SD is \(s\); the population SD is \(\sigma\).

The normal distribution

In our resampling experiments earlier, we mentioned the normal distribution. When we resample and compute the mean, for example, our results will converge to that shape.

\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}} \]

Warning

This is a probability density function. Don’t freak out about this. The important thing is to see \(\mu\) (the mean) and \(\sigma\) (the standard deviation). This just means that the probability of seeing a particular observation is is a function of the mean and SD of the distribution.

Normal PDF

What is “probabiilty density”?

For a truly continuous variable, the probability that a variable takes on an exact value (say a height of 170.0000… cm) is zero.

This is quite different than, say, the probability that a fair coin comes up heads (.5) or that a person answers “yes” to a question about abortion in a population.

Tip

You could ask the probability that a person’s height is, say, greater than or equal to 169.5 and less than 170.5. As the width of this “window” shrinks to zero, the probability also shrinks to zero. But we can talk about the density of the probability in that area.

Density can be higher than 1!

Cumulative density function

Cumulative probability

Normal distribution: wordsum

Based on what we have already computed, we can approximate the distribution of wordsum using a normal distribution with a mean of 6.36 and a SD of 2.22.

We can write this as

\[\text{wordsum} \sim \cal{N}(6.36, 2.22) \]

The first number is the mean and the second is the standard deviation.

How good is this approximation?

ECDF vs. Normal

Homework

For two separate variables with at least 10 categories:

  • calculate and interpret the mean and SD
  • superimpose a probability density plot on the histogram
  • interpret the quality of the normal approximation to the observed distribution. What does the approximation get right? What does it get wrong?
  • use some Latex math (use both inline and display math at least once)
  • use some inline R code for practice

Warning

Make your document look good. For example, label your graph axes, load only packages you actually need, and don’t allow echo or message for loading packages. The default is rendering to HTML. But you can make slides or pdf if you prefer. Try to make it clear that you are not just coping my code!

Robust statistics

In inferential statistics (making inferences from samples to populations), we focus on the mean and standard deviation.

The median is used more as a descriptive statistic. It is called a robust statistic because it is insensitive to outliers. For example, the median age in the 2022 GSS is 46. This would be true even if we took the oldest person and made them 900 years old!

Median: example

Bernoulli distribution

You’ve seen this before but some statistical distributions have only two options. If we want to describe the proportion of US adults who have a college degree, we can describe this as a Bernoulli distribution with \(p = 0.372\).

One- and two-parameter distributions

The normal distribution has two parameters, \(\mu\) and \(\sigma\). This is because the normal distribution is defined by the location of its center and the width of its spread.

The Bernoulli distribution has only one parameter, which is \(p\) (sometimes people use \(\pi\)). This is just the probability of a “yes,” or, as it is often called, a “success.”

But this doesn’t mean that the Bernoulli doesn’t have center and spread…

Spread of the Bernoulli distribution

Variance is a measure of uncertainty about where the data are. Imagine two alternatives: a Bernoulli distribution with \(p = .01\) and one with \(p = .50\). There’s a lot more uncertainty about the latter!

So the spread is also a function of \(p\). In other words, \(p\) determines both center and spread.

For a variable, \(X\), \(\text{Var}[X] = p(1-p)\). Therefore it’s also true that \(\text{SD}[X] = \sqrt{p(1-p)}\).

From Bernoulli to normal

The normal distribution can be derived as the sum of many Bernoulli trials. For example, imagine we start with 100 people standing on the halfway line of a football field. Each person flips a coin and, if it’s heads, takes a step forward (say one meter). If tails, they take a step backward (one meter). What would things look like after 100 trials?

Physical simulation

Univariate inference

Connecting to the CLT

Now that we know about the standard deviation, we are ready to combine this with what we learned earlier about the Central Limit Theorem.

Let’s look back at the simulations we did of three Bernoulli distributions with \(p = .7\) and sample sizes of 60, 250, and 1000. Recall that each one was simulated 2500 times.

Remember these?

# A tibble: 3 × 3
  sample_size     p     sd
  <chr>       <dbl>  <dbl>
1 n = 1000    0.700 0.0145
2 n = 250     0.701 0.0290
3 n = 60      0.700 0.0584

The sampling distribution

The sampling distribution is the distribution that we would get if we did simulations like these infinite times. (Again, not infinite sample size but infinite simulations of a given sample size!) Thanks to the CLT, we know exactly how these would look!

This example is from a Bernoulli distribution but this works for any distribution. Mean estimates from repeated samples would form a normal distribution with a known mean and standard deviation.

The standard error

The expected mean of the sampling distribution is just \(\bar{x}\), the sample mean. This is the best guess we can make.

The standard deviation of the sampling distribution has a special name: the standard error. The formula is

\[ \text{SE} = \frac{\text{SD}}{\sqrt{n}} \]

Note

This is one of the many cases where there is an analytic solution to a problem we could address through simulation. Use the formulas above to calculate the SEs of the simulations. How well do the empirical values match?

SE examples

Calculate the following SEs:

  • GSS age: \(\hat{s} = 17.7\), \(n = 2513\)

  • GSS wordsum: \(\hat{s} = 2.2\), \(n = 2513\)

  • GSS college: \(\hat{p} = 0.37\), \(n = 2513\)

Note

The “hat” over \(\text{SD}\) and \(p\) is a way to say explicitly that it is an estimate from a sample. This is pronounced, for example, “p-hat.”

Margin of error

When we report an estimate (for example an estimated vote proportion from a poll), we want also to report our uncertainty about that estimate because it comes from a sample.

Most people encounter this “in the wild” as the margin of error. This is conventionally calculated as plus or minus two standard errors (for reasons we will discuss below).

Calculate

What would the margin of error values be for yes/no polls with \(\hat{p} = .53\) and sample sizes of 400, 900, and 1600?

Confidence interval

Earlier in the course we looked at the interquartile range of the simulation results from sampling. That was a way to quantify how much our results could vary given our sampling set up.

But the traditional way is to use a confidence interval based on the normal distribution. Since we know how to calculate the standard error based on descriptive statistics, we can calculate an interval within which some percentage of the estimates will fall given our sampling design and descriptive results.

Width of the confidence interval

The width we choose for a confidence interval is a function of how “conservative” we want to be. For example, in a yes/no poll, we are 100% sure that \(p\) is between 0 and 1. But that’s not very useful.

The \(\pm\) 2 SE convention of the “margin of error” is based on the 95% confidence interval, which is the most conventional width now.

95% confidence interval

99% confidence interval

89% confidence interval

68% confidence interval

Aside: the z-score

The z-score is a how we refer to how many standard deviations away from the mean a particular value is. This applies everywhere the normal distribution gets used.

It’s an abstract way to talk about “weirdness” without specifying units. If a person is 5 SDs from the mean on some dimension, they are very, very weird! This is true for height, wealth, extraversion, etc.

Tip

If the mean height for men in the US is about 70 inches and the SD is about 4 inches, how tall is someone 5 SDs above the mean? Below the mean?

Interpreting confidence intervals

What most people say is “we are 95% sure the true value is between the lower and upper bound of the confidence interval.” But that’s not quite accurate.

It’s more correct to say that, if we did the same study infinite times, 95% of the computed intervals would contain the true value.

The confidence level refers to our confidence in the procedure, not the specific interval, since that is calculated from just one dataset.

Homework

  • Calculate means, SDs, and confidence intervals (89%, 95%, 99%) for one continuous and one binary variable. Interpret the confidence intervals.
  • Do two simulations (one continuous, one binary) to show that simulation-based standard deviations of the estimate converge to the formula-based standard error of the sampling distribution. Explain the result to show you understand what you did.

Univariate hypothesis test

The confidence interval is closely linked to the idea of the hypothesis test. This uses the sample data to test if there is enough evidence to assert that the population differs from some specific reference value.

This reference value is called the null hypothesis.

Hypothesis test considerations

As we’ve seen, the probability that a variable takes on an exactly specific value is, for all intents and purposes, zero. So we want to ask if the sample statistic is different from (above or below) some specific value.

In the case of yes/no polling, the most obvious null hypothesis is .5 or 50%. This is because the majority wins.

Example

Consider we are conducting a poll on a high-speed rail initiative. We want to know if it’s going to pass. This gives an obvious null hypothesis of 50%. Can we confidently assert that the actual vote numbers are going to be above or below 50%? Or is the evidence too close to 50% to tell?

Let’s say we poll 600 registered voters and estimate \(\hat{p}_{\text{yes}} = .55\). Does this give us enough evidence to say that it’s going to pass?

The null distribution

The way to approach this is to ask what the world would look like if the null hypothesis (a 50/50 split in the population) were actually true? What would the results of that world look like if we polled it infinite times?

More specifically, how often would we get a result 5 or more percentage points away from .5?

If the null were true, we’d only expect to get a value this far away from the expected null value 1.4% of the time. This is called a p-value.

Tails and tests

The unshaded area of the last graph represents 1.4% of the area of the sampling distribution. But why are we using the left and right sides? Why not just use the right side and get a p-value of 0.7%? After all, it is true that we’d only expect to get a value as large as .55 in a sample 0.7% of the time.

The use of two-tailed tests rather than one-tailed tests is ubiquitous in sociology. It’s regarded as “conservative” even though there is usually not a good rationale for it.

Note

We haven’t actually talked about how to use these for a “test” yet, but we’re close!

z-score “weirdness”

We can approach this issue more generally through z-scores. What is the standard error of the null sampling distribution? Recall that the null proportion is .5 and the sample size is 600. (It’s about .0204.)

How “weird” therefore is our result of .55? How many standard errors is it away from the expected value of the null distribution? (It’s about 2.45 SE away.)

From z-score to p-value

The probability of getting an absolute z-score of 2.45 or greater is about .014. We can get that value using R code:

(1 - pnorm(2.45)) * 2 # times 2 for high and low tails
[1] 0.01428562

This is called the p-value of the test.

Alpha level

How do we connect these ideas to a hypothesis test? To conduct a hypothesis test, we need an alpha level (or \(\alpha\) level). This is the proportion of the time we’re willing to falsely assert that the observed data did not come from the null distribution.

This is connected to the idea of type-I error or the idea of a false positive.

In the above case, for example, there is a chance (1.4%) that we could see a polling result as high as 55% (or as low as .45) with our sample size even if the population is actually 50/50.

Hypothesis test

We’re now ready for the algorithm of the hypothesis test:

  1. Choose an alpha level (say, .05)
  2. Calculate the observed sample statistic (e.g., .55)
  3. Calculate the absolute difference between the statistic and the expected value under the null (.55 - .50 = .05)
  4. Convert this difference into a z-score using the SE of the sampling distribution (z = .05 / .0204 = 2.45)
  5. Convert the z-score to a p-value (.014)
  6. If the p-value is less than alpha reject the null hypothesis; if the p-value is greater than alpha fail to reject the null hypothesis.

Writing the test

Sometimes people write a hypothesis test out formally. Here’s an example.

\[ H_0 : p = .5 \\ H_1 : p \neq .5 \]

Rejecting (or not) the null

This language can feel weird. We can never accept the null hypothesis (\(H_0\)), in part because the probability of an exact value (e.g., .5) being true is basically zero. So we can only either reject the null hypothesis or fail to reject it.

When we reject the null hypothesis, we call a result statistically significant. That’s literally all that phrase means!

Conventional alpha levels

The conventional alpha level for a test is .05. Heuristically speaking, this means we’re willing to falsely reject the null hypothesis 5% of the time. This value is by no means sacred. In fact, it is fundamentally arbitrary.

Just as we saw above with confidence intervals, we can pick any value we like, which is both liberating and scary!

p-values and confidence intervals

There is a close relationship between p-values and confidence intervals. For example, if a 95% confidence interval includes the null value, the p-value of the hypothesis test will be above .05.

In our example, the 95% confidence interval for our poll would be [.51, .59]. Since this interval does not include .5, we could decide to reject the null hypothesis on that basis.

In fact, because p-values and CIs can both be used for testing, it’s usually better to use CIs because they convey the uncertainty of the estimate as well.

Continuous variables

The same logic applies to continuous variables in exactly the same way. The only difference is the calculation of the standard error, which relies on the standard deviation.

p-value pitfalls

People sometimes say and do stupid things with p-values. Here are some tips:

  • Don’t use asterisks as informal indicators of “how big” an effect is (do you have an alpha level or not?)
  • Don’t mistake “statistical significance” for importance
  • When assessing the plausibility of a hypothesis, you need to know the prior probability of the hypothesis as well as the p-value. [Bayes’ Rule…]

Homework

Conduct four hypothesis tests (two binary, two continuous) using variables you haven’t used before. Please do the following:

  • choose a reasonable null (although this will be somewhat arbitrary in many cases)
  • go through the whole algorithm and interpret each step correctly
  • use at least two different alpha levels throughout the homework (but just one per variable)
  • compare the hypothesis test results to confidence intervals to improve your intuition
  • as always, do at least one visualization per test

Comparing Two Groups

Overview

We learned about univariate confidence intervals and tests against a point null hypothesis because they are relatively simple. But most things in social science are about comparison between groups or levels. We are going to start with two-group comparisons and then move to a more general framework in the next section.

Education and abortion rights

As usual, we will start with simulation. Let’s go back to abany. Do college-educated and non-college educated people have different levels of support for abortion rights? Let’s set up the data.

dab <- gss2022 |> 
  select(abany, degree) |> 
  drop_na() |> 
  mutate(abany = if_else(abany == 1, 1, 0),
         college = if_else(degree >= 3, "BA+", "<BA"))

Visualizing the difference

Inference to the population

In the sample, we see that there is a difference. Among those with college degrees, 0.69 support. Among those without, 0.54 support. But is there a difference in the population? We can set up the question like this:

\[ H_0: p_{\tiny{BA+}} = p_{\tiny{<BA}} \\ H_1: p_{\tiny{BA+}} \neq p_{\tiny{<BA}} \]

Test as difference

There’s another way we could set this up, however, which makes it clearer how we might test it.

\[ H_0: p_{\tiny{BA+}} - p_{\tiny{<BA}} = 0 \\ H_1: p_{\tiny{BA+}} - p_{\tiny{<BA}} \neq 0 \]

The null distribution

Testing this requires setting up a world where the proportions are the same in the two groups and then evaluating how often we get a difference as large as we do in the sample. This is very much like we did before when we set up a null polling distribution where the true value was .5 and then seeing how often we got a departure from that value as large as in the sample.

Simulation function

# based on empirical values
pooled_prop <- mean(dab$abany)
n1 <- dab |> filter(college == "BA+") |> nrow()
n2 <- dab |> filter(college == "<BA") |> nrow()

# function
## set up df and random gen abany
null_diff <- function(p, n1, n2) {
  tmp <- tibble(
    id = 1:(n1 + n2),                  # number of cases
    college = c(rep("BA+", n1),        # correct Ns
                rep("<BA", n2))) |>   
    mutate(abany = rbinom(1, 1, p),    # fake abany
           .by = id)                   # rowwise() like

## spit out diff
mean(tmp$abany[tmp$college == "BA+"]) -  
mean(tmp$abany[tmp$college == "<BA"])

}

Simulation

set.seed(722)

# draw 5000 diffs from null distribution
abany_null_sims <-
  tibble(
    sim_id = 1:2000) |> 
  mutate(diff = null_diff(pooled_prop, n1, n2),
         .by = sim_id)

Results

Interpreting the test

The simulation results vary from -0.096 to 0.091. This doesn’t exactly mean a p-value of zero, but we didn’t find any differences as large as the real data in 2000 tries.

We would certainly reject the null hypothesis of no difference under any realistic alpha level here.

Simulating the confidence interval

We could also use the real data to simulate the confidence interval of the difference. Instead of resampling from the null distribution, we can resample from the observed distribution. This is called bootstrapping.

get_diff <- function() {
  tmp <- slice_sample(dab,               # sample
                      n = nrow(dab),     # same size
                      replace = TRUE)    # with replacement
  
mean(tmp$abany[tmp$college == "BA+"]) -  # get diff
mean(tmp$abany[tmp$college == "<BA"])
}

Simulation

set.seed(722)

# draw 5000 diffs from null distribution
abany_boot_diffs <-
  tibble(
    sim_id = 1:2000) |> 
  mutate(diff = get_diff(),
         .by = sim_id)

Results

Interpretation

Here is the 99% confidence interval of the difference based on the percentile bootstrap.

quantile(abany_boot_diffs$diff, c(.005, .995)) |> 
  round(3)
 0.5% 99.5% 
0.074 0.210

Here is the 99% confidence interval based on the normal bootstrap.

obsdiff <-  # ACTUAL difference
  mean(dab$abany[dab$college == "BA+"]) -
  mean(dab$abany[dab$college == "<BA"])
bootsd <- sd(abany_boot_diffs$diff)

c(obsdiff - 2.57 * bootsd,
  obsdiff + 2.57 * bootsd) |> round(3)
[1] 0.074 0.212

Neither includes zero, suggesting a population difference.

Analytic hypothesis test

We can do these things without simulation. Here is the analytic test for a difference in proportions:

\[ Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{ \frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}} \] We just turn this z-value into a p-value and compare to alpha.

Example

Let’s use the information we have to calculate the test statistic and p-value.

p1 <- mean(dab$abany[dab$college=="BA+"])
p2 <- mean(dab$abany[dab$college=="<BA"])

zstat <- 
  (p1 - p2) /
  sqrt(p1 * (1 - p1) / n1 + p2 * (1 - p2) / n2)

zstat                     # z-statistic
[1] 5.28892
(1 - pnorm(zstat)) * 2    # two-sided p-value
[1] 1.230407e-07

Analytic confidence interval

To get a confidence interval, you need the standard error of the difference and then you just calculate it the usual way (e.g., \(\pm\) 2.57 SEs. The formula for the SE is:

\[ \text{SE}_{\text{diff}} = \sqrt{ \frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}} \]

This gives us a SE of 0.027 and a 99% CI of [0.074, 0.213]. This is quite close to the bootstrap estimates.

Extending to continuous variables

I am not going to prove to you that simulations work just as well for continuous variables. For example, we could ask whether older people really score better on wordsum.

dword <- gss2022 |> 
  select(wordsum, age) |> 
  drop_na() |> 
  mutate(agecat = if_else(age > 46, "older", "younger"))

Visualizing the difference

Visualizing the distribution

Hypothesis test

The setup for the test is very similar for means as for proportions. Only the typical Greek letter changes.

\[ H_0: \mu_{\tiny{older}} - \mu_{\tiny{younger}} = 0 \\ H_1: \mu_{\tiny{older}} - \mu_{\tiny{younger}} \neq 0 \]

Analytic solution

As we will discuss soon, we often use something called a t-test for comparing differences in means. For now, we’re going to stick with our approach based on z-scores and the normal distribution. The formula is:

\[ Z = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \]

The z-statistic is 3.952 and the p-value is 7.7421867^{-5}. Looks like the difference in the population probably isn’t exactly zero!

Analytic confidence interval

The confidence interval is the same, based on the denominator of the z-test as before:

\[ \text{SE}_{\text{diff}} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} \]

So the 99% confidence interval would be [0.12, 0.58].

Student’s t-distribution

Don’t worry too much about “degrees of freedom” (df). This means how many independent pieces of information are left after calculating means. For a two-group comparison where both groups have equal SDs, it’s roughly \(df = n-2\).

Using t-statistics

We use t-statistics the same as z-statistics: by converting them into p-values or using them as the basis of a confidence interval. With two groups of 20 and a t-statistic (difference / SE) of 2, we’d get:

# p-value
(1 - pt(2, df = 38)) * 2
[1] 0.05268507
# confidence interval width (95%)
qt(.975, df = 38)
[1] 2.024394

We would fail to reject the null with an alpha of .05 here.

Effect sizes

“Statistical significance” is just about rejecting the null hypothesis of zero difference. This is often not very impressive. We need a way of talking about how big a difference is that is not dependent on a p-value.

The effect size is a standard way of comparing two groups regardless of the units of the original variable

Example

In the 2022 GSS, college-educated respondents watch 2.69 hours of TV per day while the non-college educated watch 3.78 hours per day. That’s a difference of 1.09 hours. Is that a small or large difference?

The p-value is about \(1.5 \times 10^{-18}\), so we’re really confident the difference isn’t zero in the population. But that’s a lot about the sample size! A p-value doesn’t tell you about the size of the difference.

Visualizing the difference

Calculating the effect size

\[ d = \frac{\bar{x}_1 - \bar{x}_2}{s} \]

This is a simple measure of effect size, often called Cohen’s d. In this case it’s -0.32. (It’s negative because the college group watches less.) This is also called a standardized mean difference.

This means that there is a difference of 0.32 standard deviations between the groups.

Probability of superiority

I’ve never seen anyone in sociology report this, but one good way to think about effect size is the probability of superiority. This is the probability that a randomly selected member of the first group (college) watches TV more than a randomly selected member of the second group (no college).

The value here is 0.41 if we assume two normal distributions and 0.398 if we calculate it directly from the data. You can get these easily in R using the effectsizes package.

Power

Because effect size and “significance” are not the same thing, we need to think about the relationship between effect size and our ability to reject the null. This is called power, which is the probability of rejecting the null hypothesis given:

  1. a specific study design (e.g., two groups of 100 respondents)
  2. a specific alpha level (e.g., .05)
  3. a specified minimum effect size (e.g., .25 standard deviations)

Generally, we want power (sometimes confusingly called \(\beta\)) to be .8 or greater, although this is just as arbitrary as any other guideline.

Example

Imagine in the population there is a .25 SD difference in some outcome (e.g., wordsum score) between two groups. If we take samples of 30 from each group, how often would we be able to “detect” the difference (e.g., reject the null hypothesis)?

As you might imagine, we are going to do this via simulation first.

Simulation function

mytest <- function(n = NULL, d = NULL, alpha = NULL) {
  
  tmp1 <- tibble(group = "A", y = rnorm(mean = d,  # group A
                                        sd = 1,
                                        n = n))
  
  tmp2 <- tibble(group = "B", y = rnorm(mean = 0,  # group B
                                        sd = 1,
                                        n = n))
  
  tmp <- bind_rows(tmp1, tmp2)                     # bind together
  
  tt <- t.test(y ~ group, data = tmp)              # t-test
  
  return(if_else(tt$p.value < alpha, 1, 0))        # null rejected?
  
}

Low power simulation

Let’s do this simulation 1000 times.

set.seed(722)

mysims <- tibble(sim_id = 1:1000) |> 
  mutate(reject_null = mytest(n = 30, 
                              d = .25, 
                              alpha = .05), 
         .by = sim_id)

mean(mysims$reject_null)
[1] 0.147

We can only reject the null here about 14.7% of the time even though there’s a real difference. A study like this isn’t worth doing!

High power simulation

What if we increase the sample size of each group to 300? How does that affect our power?

set.seed(722)

mysims <- tibble(sim_id = 1:1000) |> 
  mutate(reject_null = mytest(n = 300, 
                              d = .25, 
                              alpha = .05), 
         .by = sim_id)

mean(mysims$reject_null)
[1] 0.869

We can reject the null here about 86.9% of the time. This is clearly much better!

Analytic solution

Power is important to compute, especially when we are collecting our own data. For something as simple as a t-test, we can use the base R function, power.t.test().

power.t.test(n = 30, 
             delta = .25, 
             sig.level = .05)

     Two-sample t test power calculation 

              n = 30
          delta = 0.25
             sd = 1
      sig.level = 0.05
          power = 0.1568035
    alternative = two.sided

NOTE: n is number in *each* group
power.t.test(n = 300, 
             delta = .25, 
             sig.level = .05)

     Two-sample t test power calculation 

              n = 300
          delta = 0.25
             sd = 1
      sig.level = 0.05
          power = 0.8636743
    alternative = two.sided

NOTE: n is number in *each* group

Note

Just as \(\alpha\) is the Type I (or false-positive) error rate, \(1-\beta\) is the Type II (or false-negative) error rate.

Sample size calculation

You can also do other power calculations:

How big a sample?

power.t.test(n = NULL, 
             sd = 1,
             delta = .25,
             sig.level = .05, 
             power = .8)

     Two-sample t test power calculation 

              n = 252.1281
          delta = 0.25
             sd = 1
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

NOTE: n is number in *each* group

How small an effect?

power.t.test(n = 100, 
             sd = 1, 
             delta = NULL,
             sig.level = .05, 
             power = .8)

     Two-sample t test power calculation 

              n = 100
          delta = 0.39814
             sd = 1
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

NOTE: n is number in *each* group

Summary

  • The simplest social science questions are about comparing groups.
  • Comparing means or proportions across two groups is the simplest version of this but gives you all the basic ideas.
  • The only real difference between the binary and continuous cases is the SD calculation.
  • Pay attention to effect size, not just “significance.”
  • Instead of asking “what about power?” in theory class, ask it about your research design.

Homework

Compare two groups on two binary and two continuous variables. Do hypothesis tests and confidence intervals. State the null hypotheses and the alternatives. Calculate and interpret effect sizes. To receive full credit, don’t use the same grouping variable for all four; use at least two different grouping variables.

Models

Models vs. tests

We just talked about z-tests and t-tests. You may have heard of many other statistical tests in your life, like ANOVA, chi-square, Fisher’s exact test, Wilcoxon’s rank sum test, and many others.

Instead of doing this, we are going to think of all “tests” as statistical models with different assumptions.

Functions

You have learned about functions in R, which take some input and use some kind of rule to produce an output. Like the function mean() takes a vector of numbers and gives you its mean.

In math, a function like \(y = 3x\) is similar. It takes an input (\(x\)) and produces an output (\(y\)). All statistical models are like this.

Univariate models

We can write a model for something as simple as the observed values of a single variable. Consider wordsum; if we want to write a model for each individual observation, we could write something like this:

\[ \text{wordsum}_i = \text{mean} + \text{weirdness}_i \]

This means that everyone starts at the same place and then departs from it in some way due to their “weirdness” (i.e., difference from what is typical).

Note

The mean doesn’t have a subscript because everyone shares the same one; “weirdness” does because everyone is weird in their own way.

Simplest model

We usually write such a model like this:

\[ \begin{align} y_i &= \mu + \epsilon_i \\ \epsilon_i &\sim \mathcal{N}(0, \sigma) \end{align} \]

The second line means that the “weirdness” (\(\epsilon_i\)) is normally distributed, meaning that less weirdness is more common than more weirdness!

DGPs, models, parameters

We think of this model as the data-generating process. Of course it’s very simple, but that’s why it’s a model. If we want to estimate a model, we use real sample data to get plausible estimates of the relevant parameters from the population. In this case, the things we need to estimate are \(\mu\) and \(\sigma\).

Estimates

Let’s say our outcome variable is wordsum. How can we estimate the model parameters from the GSS data?

  • \(\hat{\mu}\) = mean(dword$wordsum)
  • \(\hat{\sigma}\) = sd(dword$wordsum)

So the estimated values are 6.36 and 2.22, respectively.

The model is a model

Using lm()

Using mean() and sd() are fine now, but they are going to become useless pretty fast. We can use the lm() function instead, which allows much more complicated stuff.

Here’s the syntax for a model estimating wordsum. Don’t worry too much about the syntax yet, though ~ is how we tell R that we are giving it a formula.

mymodel <- lm(wordsum ~ 1, data = dword)

Using summary()

summary(mymodel)

Call:
lm(formula = wordsum ~ 1, data = dword)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.3594 -1.3594 -0.3594  1.6406  3.6406 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.35937    0.04414   144.1   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.222 on 2534 degrees of freedom

Note

(Intercept) gives us \(\hat{\mu}\), its SE, and the test of the zero null (which makes no sense here). The “residual standard error” is the estimate of \(\hat{\sigma}\). Ignore the dumb stars.

From t-test to model

Again, we usually want to compare two groups. That’s what we were doing with the t-test. If we want to compare the wordsum scores of older and younger respondents (like we did above) we can write it like this:

\[ \begin{align} \text{wordsum}_i &= \alpha + \beta(\text{older}_i) + \epsilon_i \\ \epsilon_i &\sim \mathcal{N}(0, \sigma) \end{align} \]

Now \(\alpha\) is \(\bar{x}_{\text{younger}}\) and \(\beta\) is the difference: \((\bar{x}_{\text{older}}- \bar{x}_{\text{younger}})\).

The null hypothesis

In this case, we have a new way of writing the null hypothesis:

\[ \mathcal{H}_0:\beta=0 \\ \mathcal{H}_1:\beta \neq 0 \]

The null hypothesis that some beta coefficient is equal to zero is pretty much your life now.

Estimating

dword <- dword |> 
  mutate(older = if_else(agecat == "older", 1, 0))
mod2 <- lm(wordsum ~ 1 + older, data = dword)     
summary(mod2)                                     

Call:
lm(formula = wordsum ~ 1 + older, data = dword)

Residuals:
   Min     1Q Median     3Q    Max 
-6.537 -1.538 -0.189  1.811  3.811 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.18904    0.06156 100.544  < 2e-16 ***
older        0.34849    0.08805   3.958 7.77e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.216 on 2533 degrees of freedom
Multiple R-squared:  0.006146,  Adjusted R-squared:  0.005754 
F-statistic: 15.67 on 1 and 2533 DF,  p-value: 7.769e-05

Tip

There’s a lot here you don’t need to worry about. The core thing to look at is the test of the beta coefficent, which is older here. How would you manually construct a confidence interval here?

Using broom::tidy()

Here’s a tidier way to look at coefficients than summary():

broom::tidy(mod2, 
            conf.int = TRUE,
            conf.level = .99)
# A tibble: 2 × 7
  term        estimate std.error statistic   p.value conf.low conf.high
  <chr>          <dbl>     <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
1 (Intercept)    6.19     0.0616    101.   0            6.03      6.35 
2 older          0.348    0.0880      3.96 0.0000777    0.122     0.575

Comparing to t-test

You can see here that the confidence interval, etc., reported by t.test() is the same.

t.test(wordsum ~ agecat, 
       data = dword,
       var.equal = TRUE,
       conf.level = .99)

    Two Sample t-test

data:  wordsum by agecat
t = 3.9579, df = 2533, p-value = 7.769e-05
alternative hypothesis: true difference in means between group older and group younger is not equal to 0
99 percent confidence interval:
 0.1215189 0.5754552
sample estimates:
  mean in group older mean in group younger 
             6.537530              6.189043

Equal variances

A regression like this assumes that the groups have equal variances. (This is why I set var.equal = TRUE in the t-test function.) This usually doesn’t matter unless you have small samples and unequal sample sizes between the two groups.

Homework

Please build on and extend the homework that was due this week. I will count this homework for BOTH week 7 and week 8. Here is what I’d like you to do:

  • keep the binary two-group comparisons as you have them already (assuming you did them already!)
  • for the continuous ones, add effect size (Cohen’s d and “probability of superiority”) to what you already have
  • add a short section on power analysis. Base your analysis on of one of the two continuous tests you calculated. Your question is: how small of an effect could I detect using these Ns and this alpha? (NOTE: your groups will not be equal sizes in the GSS. So you have the option of doing this via simulation or using something like the pwr package, which is like what you’ve learned.)
  • finally, add a second short section on power analysis that estimates the sample size you would need for an imaginary experiment. You pick the minimum interesting effect size, the alpha level, and the power level.

Models for two-group comparisons

  • continuous ~ group
  • binary ~ group
    • identity
    • log
    • log odds
  • count ~ group
  • multinomial ~ group

Binary outcomes and the Generalized Linear Model

Outcome: graduate degree (yes/no)

Predictor: at least one parent with graduate degree (yes/no)

dgrad <- gss2022 |> 
  select(degree, madeg, padeg) |> 
  mutate(grad = if_else(degree == 4, 1, 0),
           # pmax() works if there's just one missing
         pardegree = pmax(madeg, padeg, na.rm = TRUE),
         pargrad = if_else(pardegree == 4, 1, 0)) |> 
  select(grad, pargrad) |> 
  drop_na()

table(dgrad$pargrad, dgrad$grad)
   
       0    1
  0 2958  390
  1  333  180

Conditional probabilities

Calculate them and write them down. You will need them!

Writing the model

\[ \text{grad}_i = \alpha + \beta(\text{pargrad}_i) \]

Or more specifically:

\[ P(\text{grad}_i =1)= \alpha + \beta(\text{pargrad}_i) \]

Estimating in R

What is family? What is link?

mod1 <- glm(grad ~ pargrad,
            data = dgrad,
            family = binomial(link = "identity"))

summary(mod1)

Call:
glm(formula = grad ~ pargrad, family = binomial(link = "identity"), 
    data = dgrad)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 0.116487   0.005544   21.01   <2e-16 ***
pargrad     0.234390   0.021788   10.76   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 3232.2  on 3860  degrees of freedom
Residual deviance: 3074.5  on 3859  degrees of freedom
AIC: 3078.5

Number of Fisher Scoring iterations: 2

“Linear probability model”

Treating the outcome as continuous even when it’s really not.

mod2 <- lm(grad ~ pargrad,
            data = dgrad)

summary(mod2)

Call:
lm(formula = grad ~ pargrad, data = dgrad)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.3509 -0.1165 -0.1165 -0.1165  0.8835 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.116487   0.005976   19.49   <2e-16 ***
pargrad     0.234390   0.016395   14.30   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3458 on 3859 degrees of freedom
Multiple R-squared:  0.0503,    Adjusted R-squared:  0.05005 
F-statistic: 204.4 on 1 and 3859 DF,  p-value: < 2.2e-16

Thinking about \(\beta\)

\[ \beta = P(\text{grad} = 1 \mid \text{pargrad} = 1) - P(\text{grad} = 1 \mid \text{pargrad} = 0) \]

What is the unit of \(\beta\)?

Risk ratio

This is just the ratio of conditional probabilities.

\[ RR = \frac{P(\text{grad} = 1 \mid \text{pargrad} = 1)}{P(\text{grad} = 1 \mid \text{pargrad} = 0)} \]

Writing as a linear model

\[ \log(P(\text{grad}_i = 1)) = \alpha + \beta(\text{pargrad}_i) \]

Or, equivalently…

\[ P(\text{grad}_i = 1) = e^{\alpha + \beta(\text{pargrad}_i)} \]

Probability and log probability

Estimating in R

mod3 <- glm(grad ~ pargrad,
            data = dgrad,
            family = binomial(link = "log"))
summary(mod3)

Call:
glm(formula = grad ~ pargrad, family = binomial(link = "log"), 
    data = dgrad)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.14997    0.04760  -45.17   <2e-16 ***
pargrad      1.10265    0.07663   14.39   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 3232.2  on 3860  degrees of freedom
Residual deviance: 3074.5  on 3859  degrees of freedom
AIC: 3078.5

Number of Fisher Scoring iterations: 6
exp(1.10265)
[1] 3.012138

What is \(\beta\) now?

\[ \begin{align} \beta = \log(P(\text{grad} &= 1 \mid \text{pargrad} = 1)) - \\ \log(P(\text{grad} &= 1 \mid \text{pargrad} = 0)) \end{align} \]

What are the units of \(\beta\)? How to interpret?

What are odds?

Probability is…

\[ \frac{P(y = 1)}{1} \]

Odds are…

\[ \frac{P(y = 1)}{1 - P(y = 1)} \]

Probability and odds

[graph]

Odds ratio

The ratio of two odds:

\[ OR = \frac{P(y = 1 \mid x=1)}{1 - P(y = 1 \mid x = 1)} \bigg/{\frac{P(y = 1 \mid x=0)}{1 - P(y = 1 \mid x = 0)}} \]

Log odds

\[ \log\left(\frac{P(y = 1)}{1 - P(y = 1)}\right) \]

Probability and log odds

\[ \log(odds) = \log\left(\frac{p}{1 - p}\right) \]

\[ p = \frac{e^{\log(odds)}}{1 + e^{\log(odds)}} \]

Log odds ratio

The ratio of two log odds (thus, the difference):

\[ \log(OR) = \\ \log \left[ \frac{P(y = 1 \mid x=1)}{1 - P(y = 1 \mid x = 1)} \right] - \log \left[ \frac{P(y = 1 \mid x=0)}{1 - P(y = 1 \mid x=0)} \right] \]

Writing as a model

\[ \log \left( \frac{P(\text{grad}_i = 1)}{1 - P(\text{grad}_i = 1)} \right)= \alpha + \beta(\text{pargrad}_i) \]

Or, equivalently…

\[ P(\text{grad}_i = 1) = \frac{e^{\alpha + \beta(\text{pargrad}_i)}}{1 + e^{\alpha + \beta(\text{pargrad}_i)}} \]

Estimating in R

[]

What is \(\beta\)?

This is just the log odds ratio:

\[ \beta = \log \left[ \frac{P(y = 1 \mid x=1)}{1 - P(y = 1 \mid x = 1)} \right] - \log \left[ \frac{P(y = 1 \mid x=0)}{1 - P(y = 1 \mid x=0)} \right] \]